r 


^^y 
^.^►V 


-^^ 


^>' 


IMAGE  EVALUATION 
TEST  TARGET  (MT-3) 


1.0     HfUllii 

■tt  Itt    12.2 


6" 


!_• 


K<5r. 


k  M<^ 


1l* , 


A. 


Gorporatian 


aSWKTMMNSTmr 
(71*)t7»490S 


CIHM/ICMH 

Microfiche 

Series. 


CIHIVI/ICIVIH 
Collection  de 
microfiches. 


Canadian  Inatituta  for  Hiatorical  Microraproductiona  /  InatHut  Canadian  da  mlcroraproductiona  Matoriquaa 


Technical  and  Bibliographic  Notaa/Notas  tachniquaa  at  bibliographiquaa 


Tha  Instituta  has  attamptad  to  obtain  tha  baat 
original  copy  avaiiabia  for  filming.  Faatura*  of  this 
copy  which  may  ba  bibllographically  uniqua, 
which  may  altar  any  of  tha  imagaa  In  tha 
raproductisr..  or  which  may  significantly  changa 
tha  usual  mathod  of  filming,  ara  chackad  balow. 


D 


D 
D 


D 


Colourad  covars/ 
Couvartura  da  coulaur 


I     I   Covars  damagad/ 


Couvartura  andommagte 


r*n   Covara  rastorad  and/or  iaminatad/ 


Couvartura  rastaurAa  at/ou  paliiculAa 

Covar  titia  missing/ 

La  titra  da  couvartura  manqua 


^ 


I     I   Colourad  maps/ 


Cartaa  gAographiquas  an  coulaur 

Colourad  ink  (l.a.  othar  than  blua  or  black)/ 
Encra  da  coulaur  (l.a.  autra  qua  blaua  ou  noira) 


I     I   Colourad  platas  and/or  Illustrations/ 


D 


Planchas  at/ou  Illustrations  an  coulaur 

Bound  with  othar  matarial/ 
RallA  avac  d'autras  documents 

Tight  binding  may  cauaa  ahadows  or  diatortion 
along  intarior  margin/ 

La  rallura  sarrAa  paut  cauaar  da  I'ombra  ou  da  la 
distortion  la  long  da  la  marga  IntAriaura 

Blank  laavas  addad  during  raatoration  may 
appear  within  tha  text.  Whenever  poaaibia,  theae 
have  been  omitted  from  filming/ 
11  se  peut  que  certainea  pagea  bkinchee  aJoutAes 
lors  d'une  restauration  apparaiaaant  dana  la  texte, 
mala,  ioraqua  cela  Malt  poaaibla,  cea  pages  n'ont 
pea  «t«  fllmtos. 

Additional  commanta:/ 
Commentalrea  supplimantalrea: 


L'Institut  a  microfilm*  la  meilleur  exemplaira 
qu'll  iui  a  AtA  possible  de  se  procurer.  Les  dAtaiia 
da  cet  exemplaira  qui  aont  paut-Atre  uniques  du 
point  de  vue  bibliographique,  qui  peuvent  modifier 
une  Image  reproduite.  ou  qui  peuvent  exiger  une 
modification  dans  la  mAthode  normale  de  fiimage 
sent  indiqute  ci-dessous. 


D 

D 

JET 
D 

D 

D 

D 

D 

D 


Coloured  pages/ 
Pages  de  couleur 

Pages  damaged/ 
Pages  endommagAas 

Pages  restored  and/or  laminated/ 
Pages  restaurAea  at/ou  palliculAea 

Pages  discoloured,  stained  or  foxed/ 
Pages  dAcolorAes,  tachetAes  ou  pIquAes 

Pages  detached/ 
Pages  dAtachtes 

Showthrough/ 
Transparence 

Quality  of  print  varies/ 
Qualiti  in^igale  de  I'lmpreseion 

includes  supplementary  material/ 
Comprand  du  material  auppMmentaira 

Only  edition  avaiiabia/ 
Sauie  MHton  diaponlble 

Pagea  wholly  or  partially  obscured  by  errata 
aHps,  tissues,  etc.,  have  been  refllmed  to 
enaure  the  best  possible  imaga/ 
Lea  pagea  totaiement  ou  partiellement 
obscurcies  par  un  feuillet  d'errata,  une  pelure. 
etc..  ont  iti  filmies  i  nouveeu  de  fapon  A 
obtanir  la  meilleure  image  poaaiMe. 


Thia  item  la  filmed  at  tha  reduction  ratio  checked  below/ 

Ce  document  est  filmi  au  taux  de  reduction  Indiqui  cl-deeaous. 

10X  14X  ItX  22X 


30X 


I 


12X 


16X 


»X 


I 

Itail* 
I  du 
lodifier 
r  une 
Image 


18 


•rrata 
I  to 


•  palura, 
ion  A 


n 


Tha  copy  filmad  hara  haa  baan  raproducad  thanka 
to  tha  ganaroaity  of: 

Library  of  Congress 
Photoduplication  Service 

The  images  appearing  hare  are  the  beat  quality 
poaaibia  conaidaring  the  condition  and  iagibiiity 
of  the  original  copy  and  in  keeping  with  the 
filming  contrect  apacificationa. 


Original  copiea  in  printed  paper  covera  are  filmed 
beginning  with  the  front  cover  and  ending  on 
the  laat  page  with  a  printed  or  illustrated  imprea- 
aion,  or  the  back  cover  when  eppropriate.  All 
other  original  copies  are  filmed  beginning  on  the 
f  irat  page  wKh  a  printed  or  iliuatratad  imprea- 
aion,  and  ending  on  the  laat  page  with  a  printed 
or  illustrated  impreaaion. 


The  last  recorded  freme  on  each  microfiche 
ahall  contain  tha  aymbol  -^>  (meaning  "CON- 
TINUED"), or  the  aymbol  ▼  (meaning  "END"), 
whichever  appliea. 

Mapa,  platea,  charts,  etc.,  may  be  filmed  at 
different  reduction  ratioa.  Thoae  too  large  to  be 
entirely  included  in  one  expoaura  are  filmed 
beginning  in  the  upper  left  hand  comer,  left  to 
right  and  top  to  bottom,  aa  many  framae  aa 
required.  The  following  diagrama  illuatrata  the 
method: 


12  3 


L'exemplaire  film*  fut  reproduit  grice  A  la 
gAnArosit*  da: 

Library  of  Congress 
Photoduplication  Service 

Les  images  suivantes  ont  M  raproduitea  avac  la 
plus  grand  soin,  compta  tenu  de  la  condition  at 
da  la  nettetA  de  i'exempleire  filmA,  et  en 
conformity  avac  lea  conditions  du  contrat  da 
fiimaga. 

Lea  axemplairea  originaux  dont  la  couverture  en 
papier  est  ImprimAe  sont  fiimis  en  commenpant 
par  la  premier  plat  et  en  terminant  soit  par  ia 
darnlAre  page  qui  comporte  une  empreinte 
d'impreaaion  ou  d'illuatration,  aoit  par  la  aacond 
plat,  aalon  le  caa.  Toua  lea  autrea  axemplairea 
originaux  sont  filmte  en  commen^ant  par  ia 
pramlAre  pege  qui  comporte  une  empreinte 
d'impreaaion  ou  d'illustration  et  en  terminant  par 
la  darnlAre  pege  qui  comporte  une  telle 
empreinte. 

Un  dea  symbolea  suivants  apparattra  sur  la 
darnlAre  image  de  cheque  microfiche,  selon  le 
ces:  le  symbole  -^  signif le  "A  SUIVRE",  le 
symbole  V  signifie  "FIN". 

Les  cartes,  planchea.  tableaux,  etc..  peuvent  Atre 
filmia  i  dea  taux  da  rMuction  difflrenta. 
Loraque  la  document  eat  trop  grand  pour  Atra 
reproduit  en  un  aeul  cHchA,  il  eat  film*  i  partir 
de  Tangle  aupAriaur  gauche,  de  gauche  i  droite. 
et  de  haut  en  baa.  9n  prenant  la  nombre 
d'imagae  nteeaaaire.  Lea  diagrammae  auivanta 
illuatrent  la  mAthoda. 


1 

2 

3 

4 

5 

6 

■m 


wUh  theas-lneh  trimopt  «t  WMMagUm.  ins,  JumM. 


t,J^u.«tN. 


AMERICAN  8UIENCE  SEJtJES  ,  V'.^. 


ASTEONOMY 


ron 


SOUOOXjS    ^IsTID    OOIjXjBOBS 


/  BY 

SIMON  "nEWCOMB,   LL.D., 

auraiuiiraRD»(T  aximoam  ■PHmnis  ams  mautioai. 


EDWARD  S.  HOLDEN,  M.A., 

PHOVMBOB  IN   TBI   V.  8,    IIAVAIi  OBRKBTATOBT. 


V 


\eVw    ism    .nV 


NEW  YORK 
HENRY  HOLT  AND  COMPANY 

1879 


^ 


^\ 


{ 


' 


Copyright,  1870, 

BY 

HcNRT  Holt  &  Co. 


PRigg  or  JoHM  A.  Grat,  Aot., 
]8  Jacob  Strbbt. 

KBW  YORK. 


I  n 


PREFACE. 


The  following  work  is  designed  principally  for  the  use 
of  those  who  desire  to  pursue  the  study  of  Astronomy  as  a 
branch  of  liberal  education.  To  facilitate  its  use  by  stu- 
dents of  different  grades,  the  subject-matter  is  divided  into 
two  classes,  distinguished  by  the  size  of  the  type.  The 
portions  in  large  type  form  a  complete  course  for  the  use 
of  those  who  desire  only  such  a  general  knowledge  of  the 
subject  as  can  be  acquired  without  the  application  of  ad- 
vanced mathematics.  Sometimes,  especially  in  the  ear- 
lier chapters,  a  knowledge  of  elementary  trigonometry 
and  natural  philosophy  will  be  found  necessary  to  the  full 
understanding  of  this  course,  but  it  is  believed  that  it  can 
nearly  all  be  mastered  by  one  having  at  command  only 
those  geometrical  ideas  which  are  familiar  to  most  intelli- 
gent students  in  our  advanced  schools. 

The  portions  in  small  type  comprise  additions  for  the 
use  of  those  students  who  either  desire  a  more  detailed 
and  precise  knowledge  of  the  subject,  or  who  intend  to 
make  astronomy  a  special  study.  In  this,  &3  in  the  ele- 
mentary course,  the  rule  has  been  never  to  use  more  ad- 
vanced mathematical  methods  than  are  necessary  to  the 
development  of  the  subject,  but  in  some  cases  a  knowl- 
edge of  Analytic  Geometry,  in  others  of  the  Differential 
Oalculus,  and  in  others  of  elementary  Mechanics,  is  neces- 


VI 


PREFAVB. 


T 


Biirily  presupposed.  The  object  aimed  at  has  been  to  lay 
u  broad  foundation  for  furtiier  study  rather  than  to  at- 
tempt the  detailed  presentation  of  any  special  branch. 

As  some  students,  especially  in  seminaries,  may  not  de- 
sire so  extended  a  knowledge  of  the  subject  as  that  em- 
braced in  the  course  in  large  type,  the  following  hints  are 
added  for  their  benefit :  Chapter  I.,  on  the  relation  of  the 
earth  to  the  heavens,  Chapter  III.,  on  tlie  motion  of  the 
earth,  and  the  chapter  o!i  Chronology  should,  so  far  as  pos- 
sible, be  mastered  by  all.  The  remaining  parts  of  the  course 
may  be  left  to  the  selection  of  the  teacher  or  student. 
Most  persons  will  desire  to  know  something  of  the  tele- 
scope (Chapter  II.),  of  the  arrangement  of  the  solar  system 
(Chapter  I V. ,  §§  1-2,  and  Part  II. ,  Chapter  XL),  of  eclipses, 
of  the  phases  of  the  moon,  of  the  physical  constitution  of 
the  sun  (Part  II.,  Chapter  II.),  and  of  the  constellations 
(Part  III.,  Chapter  I.).  It  is  to  be  expected  that  all  will 
be  interested  in  the  subjects  of  the  planets,  comets,  and 
meteors,  treated  in  Part  II. ,  the  study  of  which  involves 
no  difficulty. 

An  acknowledgment  is  due  to  the  managers  of  the 
Clarendon  Press,  Oxford,  who  have  allowed  the  use  of  a 
number  of  electrotypes  from  Chambers's  Descriptive 
Astronomy.  Messrs.  Fauth  &  Co.,  instrument- makers,  of 
Washington,  have  also  lent  electrotypes  of  instruments, 
and  a  few  electrotypes  have  been  kindly  furnished  by  the 
editors  of  the  American  Journal  of  Science  and  of  the 
Popular  Science  Monthly.  The  greater  part  of  the  illus- 
trations have,  however,  been  prepared  expressly  for  the 
work. 


ui»Hi.-«»|]i.-^ 


>  been  to  lay 
'  than  to  at- 

branch. 
,  may  not  de- 

as  that  em- 
ing  hints  are 
elation  of  the 
lotion  of  the 
80  far  as  pos- 
}  of  the  conrso 
r  or  student. 
r  of  the  tele- 
e  solar  system 
.),  of  eclipses, 
onstitution  of 
constellations 
d  that  all  will 

comets,  and 
hich  involves 

lagers  of  the 
d  the  use  of  a 
i  Descriptive 
»nt-makerB,  of 
instruments, 
nished  by  the 
<!e  and  of  the 
rt  of  the  illus- 
resslv  for  the 


CONTENTS. 


PART  I. 


Introductior  . 


CHAPTER  I. 

THB  RBLATIOR  OF  THE  EARTH  TO  THB  HBAVENB. 

The  Enrth— The  Diurntl  Motion  uid  the  Celestial  Sphere — Corra- 
■pondence  of  the  Terrestrial  and  Celestial  Spherea  — The 
Diurnal  Motion  in  different  Latitudes— Relation  of  Time  to 
the  Sphere— Determination  of  Terrestrial  Longitudes— Mathe- 
matical Theory  of  the  Celestial  Sphere — Determination  of 
Latitudes  on  the  Earth  hj  Astronomical  Obsenrations— 
PiralUx  and  Semidiameter 9 

CHAPTER  n. 

ABTROHOiaCAL  IHBTRTTHBim. 

The  Refracting  Telescope-ReflectingTelesoopes— Chronometers 
and  Clocks— The  Transit  Instrument— Graduated  Circles— 
The  Meridian  Circle— The  Equatorial— The  Zenith  Telescope 
—The  Sextant 58 


CHAPTER  in. 

MOTION  OF  THB  BABTH. 

Ancient  Ideas  of  the  Planets— Annual  Revolntlon  of  the  Earth— 
The  Sun's  apparent  Path— OS-iqoity  of  the  Ecliptic— The 
Senwns »« 

CHAPTER  IV, 

THB  FI.A1TRTART  KOTIONB. 

Apparent  and  Real  Motions  of  the  Planets— GraTltation  in  the 
Heavens— Kbflbr's  Laws  of  Planetary  Motion Ill 


MMn 


viii 


aONTBNTS. 


CHAPTER  V. 

UNITKRHAL  OBAVITATIOH. 

FAOB 

NbwtoN'h  L»w8of  Motion— Froblema  of  QimvlUtlon—ReBultB  of 
Uravitation— ReiuarkB  on  the  Theory  of  QraviUtion 181 

CHAPTER  VI. 

THE  MOTION  AND  ATTBACTION  OF  THK  MOON. 

The  Mooii'b  Motion  and  PhaBcB— The  Sun'B  disturbing  Force- 
Motion  of  the  Moon's  Nodes — Motion  of  the  Perigee— Rotation 
of  the  Moon— The  Tides 16S 

CHAPTER  VII. 

HCLIFSKS  or  THK  BUN  AND    MOON. 

The  Earth's  Shadow  and  Penumbra — EclipseB  of  the  Moon — 
Eclipses  of  the  Bun — The  Recurrence  of  Eclipses — Cliaracter 
of  EclipseB 168 

CHAPTER  Vra. 

THE  EARTH. 

Mass  and  Density  of  the  Eartli — Laws  of  Terrestrial  Gravitation — 
Figure  and  Magnitude  of  the  Eartli — Change  of  Oravitj  with 
the  Latitude — Motion  of  the  Earth's  Axis,  or  PreoesBion  of  the 
Equinoxes 188 

CHAPTER  IX. 

OBUBSTLAIi  HBABURBKBNTfl  OF  XABS  AND  DIBTANOI. 

The  Celeatial  Scale  of  Measurement— MeaaareB  of  the  Solar 
Parallax— Relative  MaaBes  of  the  Sun  and  Planets 218 

CHAPTER  X. 

THE  BBFBAOTION  AND  ABEBBATION  OF  LIGHT. 

AtmoBpheric  Refraction— Aberration  uid  the  Motion  of  Light 284 

CHAPTER  XL 
OHBONOIjOOT. 

ABtronomical  Measureb  of  Time  —  Formation  of  Oalendan  — 
DiviBion  of  the  Daj — Remarks  on  improving  the  Calendar — 
The  Astronomical  Ephemeris  or  Nautical  Almanac. . , 245 


FAOB 

-ResultB  of 
>n 181 

>ON. 

ng  Force — 
B — Rotation 
lt» 

,he  Moon — 
—Character 
168 

ravitation — 
(ravlty  with 
BMion  of  the 
188 

iTAlTCT. 

the    Solar 
1 818 

lOHT. 

f  Light 884 

MendarB  — 
9  Calendar — 

10. 845 


V0NTENT8. 

PART  II. 

TIIE  SOLAR  SYSTEM  IN   DETAIL 


I.V 


aiAPTEU  I. 

PAOB 

Stbiicturk  of  the  Solak  System 267 

CHAPTER  II. 

THE    HUN. 

General  Sammarf— The  PliotoHphere— Sun-Spots  and  Pacute— 
The  Sun'ii  Chromospliere  and  Corona—Bources  of  the  Sun'a 
Heat 278 

CHAPTER  III. 

THB  IKTBRIOn  VhKSVn. 

Motions  and  Aspects —Aspect  and  RoUtion  of  Mercury  — The 
Aspect  and  supposed  Rotation  of  Venus— Transits  of  Mercury 
and  Venus — Supposed  intramercnrial  Planets 810 

CHAPTER  IV. 
The  Moon 886 

CHAPTER  V. 

THE  PLANBT  MAB8. 

The  Doscriotion  of  the  Planet— Satellites  of  Mars 884 

CHAPTER  VI. 
The  Minor  Planktb 840 

CHAPTER  VII. 

JCFITBR  AND  HIS  BATBI.LITB8. 

The  Planet  Jupiter— The  Satellites  of  Jupiter 848 

CHAPTER  VIII. 

>  BATTRN  AND  HIB  BTBTBIC. 

Gtoneral  Description— The  Rings  of  Saturn— Satellites  of  Satnm. .  8SS 


llil 


'ife;..  j  --:  -K-ffm^^p-.sv''.i 


X  VQHTKMti. 

CHAPTER   IX. 
Tub  PI.ANKT  Ukaniis— BatuIIitM  of  Ursniu. UOa 

CHAPTER  X. 
TiiK  Pi.AMvr  Nbitonb— Hatellitu  of  Neptune 800 

CHAPTER  XI. 
Tub  Phybioal  Constitution  of  tub  Plambts 870 

CHAPTER  XII. 

MBTEORB. 

Plionomena  and  Cauwa  of  Metoorn — Meteoric  Skowera 870 

CHAPTER  XIII. 

COMBTB. 

Aipect  of  CometB— The  Vaporous  EnvelopeB— Tlie  Physical  Con- 
stitution of  Comets — Motion  of  Comets — Origin  of  Comets — 
Remarkable  Comets 888 


PART   III. 

TIIE  UNIVERSE  AT  LARGE. 


Introddction *11 

CHAPTER  I. 

THB  OOnSTBLIiATIOIIB. 

General  Aspect  of  the  Heavens— Magnitude  of  the  BUre— The 
Constellations  and  Names  of  the  Stars— Deacriptlon  of  Con- 
stellations—Numbering and  Cataloguing  the  Stars 410 

CHAPTER  n. 

VARIABT'B  AKD  TBHPOHABT  BTAIW. 

Stars  Regularly  Variable— Temporary  or  New  SUrs—Theoiy  of 
Variable  Stars **® 


VONTKNTS.  «^ 

(!HAPTKU  III. 

MIII.TII'I.K   MTAIIX. 

PAOl 

Character  of  Doable  »nd  Multlj.k  8tar»-()rbll«  ..f  Binary  KtarH. .  44M 

CHAl'TKH   IV. 

MRBUL/K  AND  CI.IIMTKUC. 

Dlncovory  of  Nebulie— (naMlflcatlon  of  Nebulas  and  Cluatera— 
Htar  Clu«teni-H|H)ttra  of  Nebula>  and  CluHtern-Dlstribuilon 
of    Nebul*  and   Cluatera  on  the  Surface  of  tho  Celestial 

_  ,   „  457 

Sphere 

CHAl'TEK  V. 

BPKCTRA  or  FIXKD  ilTARB. 

Charactera  of  Stellar  Spectra— Motion  of  SUra  In  the  Line  of  Sight.  4fl8 

CHAPTEK  VI. 

MOTIONB  AKD  DIBTANCKB  OF  THR  BTAR8. 

Proper  Motlona— Proper  Motion  of   the  Bun— Dbtances  of  the 
Fixed  Stan ^'^ 

CHAPTER  VII. 

CiOIIBTRUCTION  0»  THH  HBAVRHB *'^ 

CHAPTER  Vlll. 

COSMOOONT 

Index «» 


f 


"'^jfi^'-Tavi'-'^"^-*'.'''^^'''-^"'^''"'""'^" •' '  '"^~~'-'''''^ 


I 


'  ;ieiiiW»;«W«»^«"IMlMratli')M 


iiiiiiiiliilliiiiJiMii'HliW 


ASTRONOMY, 


INTRODUCTION. 

AsTROKOMT  {pKttrfp — a  star,  and  ko'/ios — ^a  law)  ia  the 
science  which  has  to  do  with  the  heavenly  bodies,  their 
appearances,  their  nature,  and  the  laws  governing  their 
real  and  their  apparent  motions. 

In  approaching  the  study  of  th  the  most  ancient  of  thd 
sciences  depending  upon  observation,  it  must  be  borne  in 
mind  that  its  progress  is  most  intimately  connected  with 
that  of  the  race,  it  having  always  been  the  basis  of  geog- 
raphy and  navigation,  and  the  soul  of  chronology.  Some 
of  the  chief  advances  and  discoveries  in  abstract  mathe- 
matics have  been  made  in  its  service,  and  the  methods 
both  of  observation  and  analysis  once  peculiar  to  its  prac- 
tice now  furnish  the  firm  bases  upon  which  rest  that  great 
g^up  of  exact  sciences  which  we  call  physics. 

It  is  more  important  to  the  student  that  he  should  be- 
come penetrated  with  the  spirit  of  the  methods  of  astron- 
omy than  that  he  should  recollect  its  minntisa,  and  it  is 
most  important  that  the  knowledge  which  he  may  gain 
from  this  or  other  books  should  be  referred  by  him  to  its 
true  sources.  For  example,  it  will  often  be  necepaiy  to 
speak  of  certain  planes  or  circles,  the  ecliptic,  the  equa- 
tor, the  meridian,  etc.,  and  of  the  relation  of  the  appa- 
rent positions  of  stars  and  planets  to  them  ;  but  his  labor 
will  be  useless  if  it  has  not  succeeded  in  pving  him  a 
precise  notion  of  these  circles  and  planes  as  they  exist  in 


ASTRONOMT. 


the  sky,  and  not  merely  in  the  ligures  of  his  text -book. 
Above  all,  the  study  of  this  science,  in  which  not  a  single 
step  coald  have  been  taken  Avithont  careful  and  painstak- 
ing observatioB' of  the  heavens,  should  lead  its  student 
himself  to  attentively  regard  the  phenomena  daily  and 
hourly  presented  to  him  by  the  heavens. 

Does  the  sun  set  daily  in  the  same  point  of  the  hori- 
zon ?  Does  a  change  of  his  own  station  afFect  this  and 
other  aspects  of  the  sky  2  At  what  time  does  the  full 
moon  rise  ?  Which  way  are  the  horns  of  the  young 
moon  pointed  ?  These  and  a  thousand  other  questions 
are  already  answered  by  the  observant  eyes  of  the  an- 
cients, who  discovered  not  only  the  existence,  but  the 
motions,  of  the  various  planets,  and  gave  special  names  to 
no  lees  than  fourscore  stars.  The  modem  pupil  is  more 
richly  equipped  for  observation  than  the  ancient  philoso- 
pher. If  one  could  have  put  a  mere  opera-glass  in  the 
hands  of  Hipparohus  the  world  need  not  have  waited  two 
thousand  years  to  know  the  nature  of  that  early  mystery, 
the  Milky  Way,  nor  would  it  have  required  a  Galilbo  to 
discover  the  phases  of  Venus  and  the  spots  on  the  sun. 

From  the  earliest  times  the  science  has  steadily  progress- 
ed by  means  of  faithful  observation  and  soimd  reasoning 
upon  the  data  which  observation  gives.  The  advances  in 
our  special  knowledge  of  this  science  have  made  it  con- 
venient to  regard  it  as  divided  into  certain  portions,  whioh 
it  is  often  convenient  to  consider  separately,  although  the 
boundaries  cannot  be  precisely  fixed. 

SphArioal  and  Praotiottl  Astronomy. — ^First  in  logical 
order  we  have  the  instruments  and  methods  by  which  the 
positions  of  the  heavenly  bodies  are  determined  from  obser- 
vation, and  by  which  geographical  positions  are  also  fixed. 
The  branch  whidi  treats  of  these  is  called  spherical  and 
practical  astronomy.  Sf^erical  astronomy  provides  the 
mathematioal  theory,  mA  practical  astronomy  (whioh  is 
almost  as  mudi  an  art  as  a  soienoe)  treats  of  the  applioap 
tion  of  this  theory. 


'J 


orHmajt.   i'j*ivJ^tj|BHjyy 


ii 


DIVIBIONS  OF  TBE  SUBJECT. 


i 


8  text  book, 
not  a  single 
id  painstak- 
its  Btudent 
a  daily  and 

of  the  hori- 
fect  this  and 
ioes  the  full 
>f  the  young 
ler  questions 
I  of  the  an- 
ice,  but  the 
icial  names  to 
pupil  is  more 
sient  philoso- 
i-glass  in  the 
ve  waited  two 
sarly  mystery, 
a  Gauleo  to 
on  the  sun. 
idily  progress- 
imd  reasoning 
le  advances  in 
made  it  con- 
lortions,  which 
,  although  the 

irst  in  logical 
)  by  which  the 
ed  from  obser- 

are  ako  fixed. 

spherical  and 
r  providas  the 
>my  (which  i» 
of  the  appiioar 


Theorttioal  Astronomy  deals  with  the  laws  of  motion  of 
the  celestial  bodies  as  determined  by  repeated  observiitiong 
of  their  positions,  and  by  the  laws  according  Jo  which  they 
ought  to  move  under  the  influence  of  their'Inutual  gravi- 
tation. The  purely  mathematical  part  of  the  science,  by 
which  the  luws  of  the  celestial  motions  are  deduced  from 
the  theory  of  gravitation  alone,  is  also  called  Celestial 
Jfechaniet,  a  term  first  applied  by  La  Place  in  the  title  of 
his  great  work  JHecanique  CeleHe. 

OownloSil  FhysiaB.— A  third  branch  which  has  received 
its  greatest  developments  in  quite  recent  times  may  be 
called  CosmiocH  Physics.  Physical  astronomy  might  be 
a  better  appellation,  were  it  not  sometimes  applied  to 
celestial  mechanics.  This  brandi  treats  of  the  physiqal 
constitution  and  aspects  of  the  heavenly  bodies  as  investi- 
gated with  the  telescope,  the  spectroscope,  etc. 

We  thus  have  three  great  branches  which  run  into  each 
other  by  insensible  gradations,  but  under  which  a  large 
part  of  the  astronomical  research  of  the  present  day  may 
be  included.  In  a  work  like  the  present,  however,  it 
will  not  be  advisable  to  follow  strictly  this  order  of  sub- 
jects ;  wc  shall  rather  strive  to  present  the  whole  subject 
in  the  order  in  which  it  can  best  be  undentood.  This 
order  will  be  somewhat  like  that  in  which  the  knowl- 
edge has  been  actually  acquired  by  the  astroncnners  of 
different  ages. 

Owing  to  the  frequency  with  which  we  hAve  to  use 
terms  expressing  angular  oieasnra,  or  ref anring  to  droles 
on  a  sphere,  it  may  be  admissible,  at  the  outset,  to  give 
an  idea  of  these  terms,  and  to  recapitulate  some  prop* 
erties  of  the  sphere. 

Aniwler  IbMaiea. — ^The  unit  of  angular  measure  most 
used  for  oonsidaiible  ang^  is  the  degree,  840  of  which 
extend  round  the  eiiele.  The  reader  knows  that  it  is  90" 
tnuk  the  horiaon  to  the  aodth,  and  that  two  objeele  180? 
apart  are  diametrioally  opposite.    An  idea  of  distanoes  of 


T 


4  ASTttOItOMY. 

a  few  degrees  may  l)e  obtained  by  looking  at  the  two  Btars 
which  fonn  the  pointers  in  the  constellation  Urm  Major 
(the  Dipper),  soon  to  be  described.  These  stars  are  5° 
apart.  The  angular  diameters  of  the  sun  and  moon  are 
each  a  little  more  than  half  a  degree,  or  30'. 

An  object  subtending  an  angle  of  only  one  minute  ap- 
pears as  a  point  rather  than  a  disk,  but  is  still  plainly  vis- 
ible to  the  ordinary  eye.  Helmholtz  finds  that  if  two 
minute  points  are  nearer  together  than  about  1'  12',  no 
eye  can  any  longer  distinguish  them  as  two.  If  the  ob- 
jects are  not  plainly  visible— if  they  are  small  stars,  for 
instance,  they  may  have  to  be  separated  3',  5',  or  even 
10',  to  be  seen  as  separate  objects.  Near  the  star  a  Lyra 
are  a  pair  of  stars  3^'  apart,  which  can  be  separated  only 
by  very  good  eyes. 

If  the  object  bo  nf>t  a  point,  but  a  long  line,  it  may  be 
seen  by  a  gootl  eye  when  its  breadth  snbtends  an  angle  of 
only  a  fraction  of  a  minute  ;  the  limit  probably  ranges 
from  10'  to  15'. 

If  the  object  lie  much  brighter  than  the  background  on 
which  it  is  seen,  there  is  no  limit  below  which  it  is  neoes- 
sarily  invisible.  Its  visibility  then  depends  solely  on  the 
qnantity  of  light  which  it  sends  to  the  eye.  It  is  not 
likely  that  the  brightest  stars  subtend  an  an^eofT^^  of 

a  second. 

So  long  as  the  angle  subtended  by  an  object  is  nmU,  we 
may  regard  it  as  varying  directly  as  the  linear  magnitude 
of  the  body,  and  inversely  as  its  distance  from  the  ob- 
server. A  line  seen  perpendicularly  snbtends  an  wo^ 
of  1°  when  it  is  a  little  less  than  60  times  its  length  dis- 
tant from  the  observer  (more  exactly  when  it  i»  67-8 
lengths  distant) ;  an  angle  of  1'  when  it  is  8488  lengths 
distant,  and  of  1'  when  it  is  206866  lengths  distsnt. 
These  numbers  are  obtained  by  dividing  the  number  of 
degrees,  minutes,  and  seoonds,  respectively,  in  the  cir- 
cnmferenoe,  by  2  x  814169966,  the  mtio  of  the  droom^ 
ference  of  a  circle  to  tlie  radius. 


»ii*li«<Ml 


iie  two  Btara 
7r»a  Major 
stare  are  5° 
d  moon  are 

minute  ap- 
plainly  vis- 
that  if  two 
1 1'  12',  no 
If  the  ob- 
lU  starB,  for 
5',  or  even 
star  a  Lyra 
parated  only 

B,  it  may  be 

an  angle  of 

mbly  ranges 

ckground  on 
1  it  is  neoes- 
lolely  on  the 
I.  It  is  not 
fie  of  x^  of 

t  is  small,  we 
tr  magnitude 
rom  the  ob- 
nds  an  angle 
to  loigth  dis- 
m  it  is  67-8 
8488l0DgibB 
^gths  cHittnt. 
le  number  of 
r,  in  the  eir- 
{  the  dream- 


CmCLEa  OF  THE  spiimE.  * 

Oreat  Cirele.  of  t.e  8phere.-In  FJg^  1  let^tho  -^no 
represent  iW  oi  a  ^Pj^'  ^Id  eti  ^  These  cir- 
the  two  great  circles  AEBJ  ^^^^  passing  through  the 

from  eveiy  point  of  the  eade -A  it  Ji  .r. 


^^  „  4.  «W»J^.  w.*  «*  « ^  ^  the  -me 
fraoe  between  the  pote.  P  «  or  r^  I-^^t  repre«>i>to- 

sphere. 


SYMBOLS  AND  ABBREVIATIONS. 


w 


«IOH8  or  THB  PLAMRS,  STC. 


0 

I  or  i 


The  Boa. 
The  Moon. 
MefCBiy* 
Veoot. 
TheEuth. 


i  Man. 

21  Jniriter. 

«  Sfttani. 

S  Uruiu. 

^  Neptane. 


The  asteraidfl  uedltttagnMied  by  a  drele  iBdodag  n  number.  whl«h 
number  indicates  the  older  of  dlMsovenr,  or  by  thdr  BMneB,  or  br  both. 
fu^iHeeate  ' 


UONB  or  THB  womjko. 


Spring 
eigne. 


(a 


T  Ariee. 
V  Tanme. 
n  Gemini. 
Sammer  { t  ®  Ctacer. 


it.  Slhw. 


Virgo. 


Antamn 
eigne. 

Winter 
rigns. 


CIO.  V3 
(13.  X 


^  Libri 
111  Sflorpina 
t  Sagittarina. 
V3  Caprieorana. 

Aqoariiuk 
X  Piaeeiw 


AinDon. 

6  Oonjanetioo,  or  having  the  ewae  loafrltnde  or  right  aaoearion. 

a  Qoadratore,  or  diflbring  fK>°  in  "  - 

9  t^poaitioB,  or  difibring  180*  la  ■•  '•  «• 


inmber,whldi 
M,or  by  both, 


llM. 

iirt>ina 
gitUriaa. 
prieoraua. 
lOAriiuk 


AaTBONOMWAL  SYMBOLS. 


Q  Ascending  node. 
n  Descending  node. 
N.  North.    8.  South. 
E.  Bust.    W.  WlBt. 

"  Degree*. 

'  Minutes  of  uc 

'  Seconds  of  »rc. 

*>  Hours. 

»  Minutes  of  time. 
.  Seconds  of  time. 

L.  Mesn  longitude  of  »  body 

g,  Mesn  nnoinsly. 
f.  True  snomnly. 


R^.  or  rt.  Bight  ascension. 

Dec.  or  6.  Decllnstion. 
r  True  senlth  distance, 
r  Apparent  «nith  distance. 
^Dirtance  from  the  earth. 
J  Heliocentric  longitude. 
6,  Heliocentric  latitude. 
X  Oeocisffltrlclongltude. 

a  t4eooentric  latitude. 

2'o,^  Longitude  of   ascending 

Undtationol  orbit  to  the  eclii.. 
tie. 


a  Mean  anomaly.  «>. 

/[True anomaly.  .„  »  unit U.  An8»»"  ^'•»"""  *"""  ^ 

i:  Mean  sidereal  motion  in  *  unit  «.     ^g  ^  ^^  ^^^ 

of  time.  L  Distance  from  node,  or  argu 

r,  Radius  vector.  |   '     ^ent  for  latitude. 

^,  Angle  of  e««'»t'*7y„„„    ,,i«, ! «.  Altitude. 
;:LoSgltude  of  perihelion   C^""  |  ^^i^.th. 

'*^^"^'  p.  Earth'sBquatorlal  radius. 

familiar  with  It  In  reading  the  pans 

occur :  lAsttars.        Rmms. 

L.tt«n.        VuMM.  J,  ^  Ku 

A  a  Alpha 

Y  yC        Oamma 

E  (  Bpsllon 

ZCi         »»• 
H«  »»• 

e  «  0        Th«ta 

li  I«» 

K «  K»PP», 

j^  X  Lambda 

Mm  Bfu 


THE  METRIC  SYSTEM, 

Thb  metrle  .y-tem  of  weight,  and  measure,  being  en>PW«i  «« 
J.  volume,  the  following  relations  between  the  unit,  of  thl.  .y.tem 
mcl  ;ied  aid  th««  of  our  oidiowy  ou.  will  b.  found  conrenlent  for 
reference : 

MRABURRS  or  LBMOTH. 

1  kilometre    =  1000  metres        ^    0  02187  mile. 
1  metre  =  the  unit  =  89  87  inches 

1  millimetre  =  TiAnr  of  a  metre  =    008987  Inch. 


HKASUREB  OF  WEIGHT. 

1  mlllier  or  tonneau  =  1.000.000  gramme.  =  8304-6  pounds. 

!"•''-••"'-•   -ther*""""':  i^rg^nr 

1  K^Lnme         =  W»»  of  a  gramme    =       001648  grain. 


The  fbllowing  rough  approximation,  may  be  memoriied : 

The  kUometfe  i.  a  little  more  than  A  of  a  mUe.  but  leM  than  |  of 

imile. 
The  mile  i.  lV\r  Ulometies. 
The  kilogramme  I.  H  pound.. 
The  pound  i.  lew  than  half  a  kilogramme. 


wing  employed  \n 
mlU  of  this  Kjtttm 
and  oonTenlent  for 


3187  mile. 
7  incbeii. 
8037  incli. 


1204-6  pounds. 
2  3046  pounds. 
15-482  grains. 
0- 01548  gntn. 


aemoriied : 

He,  but  Itm  tliu  |  of 


CHAPTER  I. 

,„K    HK..T.O.    -J„B^ -KT„   TO    THB 
$i  1.  THB   EABTH. 

U  considering  the  n^ladon  of  «;« -f^J^.tolTm^^ 
we  iieceBearily  l>egin  r:f\'^l,t^\ChL:yXhJJ, 

n'3eS*:f':;St;wn  fact,  will  show  th^  this 
eih'l^u  which  we  live  is,  at  least  approxiuiately,  > 
Klobe  whose  dimensions  are  gigantic  ^.hM^^^ 
when  compared  to  onr  ordinary  aiid 
daily  ide«.  of  si«».    If  «^P«^^ 
Mveral  ways  known  to  he  nearly  | 

that  of  a  sphere.  , 

I  It  haa  been  repeatedly  circum- 

navigated  in  various  directions. 

II  Portions  of  its  swrface,  via- 
ble from  elevated  positions  in  the 

midst  of  extensive  phihis  or  at  sea,  

Zoeu  to  be  hounded  by  circles.  T^Jl^^^ 

IWppemnce  at  all  points  of  the  j^TtS^^^:. 
sorfw*  Ta  body  i.  a  geometnca'  f^,,^^^tSSlXi&^ 
attribute  of  a  globufar  form  only.      _  . 

m   Fortlier  than  this  we  know  thrt  «*»tui  ""»" 

geodetie  surveys  have  agreed  with  this  general  wu 


g(magggBj^y^:F'^''^g^^^WW^^''*^*'^^ 


^N*"* 


10 


ASTHONOMT. 


More  procisct  reasonH  will  li«  apparent  later,  but  those  will 
be  Buttioient  to  base  our  general  considerations  npon.  Of 
the  aize  of  the  earth  we  may  form  a  rongh  idea  by  the 
time  re(|uired  to  travel  completely  around  it,  which  is 
now  about  three  months. 

We  find  next  that  this  globe  Ih  completely  isolated 
in  space.  It  neither  rests  on  any  thing  else,  nor  is  it  in 
contact  with  any  surrounding  body.  The  most  obvious 
proof  of  this  which  presents  itself  is,  that  mankind  have 
visited  nearly  every  part  of  its  surface  without  finding 
any  such  connection,  and  that  the  heavenly  bodies  seem 
to  perform  complete  circuits  around  it  and  under  it  with- 
out meeting  with  any  obstacles.  The  sun  which  rose  to- 
day is  the  same  body  as  the  setting  sun  of  yestetrlay,  but 
it  has  been  seen  to  move  (apparently)  about  the  earth 
from  east  to  west  during  the  day,  and  it  regulariy  reap- 
pears each  morning.  Moreover,  if  attentively  watched, 
it  will  be  found  to  rise  and  set  at  different  parts  of  the 
horizon  of  any  place  at  different  times  of  the  year,  which 
negatives  the  ancient  lielief  that  its  nocturnal  joiirney  was 
made  through  a  huge  subterranean  tunnel. 

%  1.  THS  DZUBITAL  KOnON  AlTD  THB  CODUnTIAIi 


PaisiDg  now  from  the  earth  to  the  heavens,  and  vMwing 
the  son  by  day,  or  the  stars  by  n^t,  the  first  ]^ienomeiKm 
whidi  fMam  our  attention  is  that  of  the  divmal  motkm. 

Wemwt  here  cantion  the  reader  to  carefnllj  distin- 
goiah  between  apparent  and  reed  motions.  For  examine, 
when  the  phenomena  of  the  dinnuU  motion  are  aet  forth 
as  real  visible  motions,  he  must  be  prepared  to  ^um  rab- 
seqnentiy  that  this  appearaneo^  which  is  obvioM  to  all,  is 
yet  a  oonseqnenoe  of  a  real  motion  only  to  be  detected  by 
reason.  We  shall  first  describe  the  dinmal  motkm  as  it 
appewn,  and  show  that  all  the  appearaaoes  to  »  qieotator 
at  any  one  place  may  be  reproaonlBd  by  8a|i|Kiiii%  the 
earth  to  remain  fixed  in  spaoe,  and  the  wM*  otnoave  of 


I 

1 
1 
t 
1 
r 
t 
ii 
li 
t 
si 
n 
I 
si 
t^ 
tl 

HT 
t( 
s« 
it 
ii. 
tl 
tl 


it  t))om]  will 
I  npon.  Of 
idoa  by  the 
t,  which  is 

ely  isolftted 
nor  is  it  in 
io8t  obviooH 
aikind  have 
ont  finding 
IxMlies  seem 
idor  it  with- 
ich  rose  to- 
fiterday,  but 
it  the  earth 
ulariy  reap- 
)ly  watched, 
)art8  of  the 
year,  which 
joiirney  was 


andTWwing 
dienomeiM» 
tlmoikm. 
folly  diatiii- 
Bxample, 
re  aet  forth 

lewninb- 
ns  toall,i8 
d0t6otod  by 
motion  as  it 

Aspeotator 
iipoiog  the 

oeoeaTeof 


TI/K  DIURNAL  MOTION. 


11 


the  noavoiiH  to  turn  abont  it,  and  finally  it  will  be  shown 
that  we  have  reason  to  Iwlieve  that  tlio  solid  uarth  itself 
is  in  constant  rotation  while  the  heavens  runmin  immov- 
ablo,  pruHunting  different  portions  in  tnm  to  the  obsorvor. 
The  motion  in  (piestSon  is  most  obvious  in  the  case  of  the 
sun,  which  appears  to  make  a  daily  circuit  in  the  heavens, 
rising  in  the  vast,  passing  over  toward  the  south,  setting  in 
the  west,  and  inovhig  around  under  the  earth  until  it 
reaches  the  eastern  horizon  again.  Observations  of  the  stars 
made  through  any  one  evening  show  that  they  also  appear 
to  perform  a  similar  circuit.  Wliatevor  stars  we  see  near 
the  eastern  horizon  will  be  found  constantly  rising  higher, 
and  moving  toward  the  south,  while  those  in  the  west 
will  be  constantly  setting.  If  we  watch  a  star  which  is 
rising  at  the  same  point  of  the  horizon  where  the  sun 
rises,  we  shall  find  it  to  pursue  nearly  the  same  ooune  in 
the  heavens  through  the  night  that  the  sun  follows 
through  the  day.  Continued  obaervations  will  show, 
however,  that  there  are  some  stars  which  do  not  let  at  all — 
namely,  those  in  the  north.  Instead  of  rising  and  letting, 
they  appear  to  perform  a  daily  revolution  around  a  point 
in  the  heavens  which  in  onr  latitudes  is  neariy  half  way 
between  the  senith  and  die  northern  horizon.  Thla  oen- 
tral  point  i»  called  the  pole  of  the  heavens.  Near  it  is 
situated  Polarity  or  the  pole  star.  It  may  be  recog- 
nized by  the  Poinier»t  two  atars  in  the  oonstelktion 
Ur»a  Mt^cTt  famiHarly  known  aa  TKe  Dipper.  These 
stars  are  ahown  in  Fig.  8.  If  we  wateh  any  star  be- 
tween the  pole  and  the  north  horizon,  we  shall  find 
that  instead  of  moving  from  east  to  west,  aa  the  stars 
generally  appear  to  move,  it  really  appears  to  move 
toward  tiie  east ;  but  instead  of  oontinning  its  motion  and 
setting  in  the  east,  we  shall  find  that  it  gradnally  dUres 
its  course  upward.  If  we  could  follow  it  for  twenty-four 
hours  we  should  see  it  move  upwards  in  the  north-east,  and 
then  pen  over  toward  the  west  between  the  zenith  ai^ 
the  pole,  then  sink  down  in  the  north-west ;  and  on  the 


,TVi'/-*wrpjv..w*'j  3^' 


II 


Asrnnmmrr. 


following  night  cnrvo  itH  couno  onco  nu.^o  toward  tho 
east.  The  arc  which  it  appears  to  deflcrilH)  in  a  perfect 
eircle,  having  tho  pole  in  its  centre.  The  farther  ffom 
the  pole  we  go,  the  larger  the  circle  which  each  star  aeeina 
to  describe  ;  and  when  we  get  to  a  distance  equal  to  that 
between  the  pole  and  tho  horizon,  each  star  in  its 
rent  passage  below  the  pole  just  grazus  41h)  horizon. 


8.— rm  APPABBMT  DiniMAI.  MonoM. 


As  a  result  of  this  apparent  motion,  each  individual 
constellation  changes  its  configuration  with  respeot  to  the 
horizon,  that  part  which  is  highest  when  the  oonstellatitm 
is  above  the  pole  being  lowest  when  below  it.  This  is 
shown  in  Figure  4,  which  represents  a  supposed  omMtel- 
lation  at  five  different  times  oi  the  night. 

Going  farther  still  from  the  pole,  tiie  stars  will  dip  be* 


11- 


THK  DIURNAL  MOTION. 


M 


toward  the 
I  a  porfeot 
rther  fi-om 
1  star  seeina 
[ual  to  that 
n  its 
izon. 


indiTidnal 
ipeoktothe 
»tMteIlati(m 
it.  This  is 
led  omistel- 

Hrill  dip  be> 


,„,  the  .,«ri.on  anring  a  portion  o^  ^  " C:^!  t  »t 
,,„„.|,y  „crc«>,ng  ^''-«Jl,v„«,d  on.  hJ(  Wow 
r!l""'«»  J[t;^S  iirwlLn,  «.d  tUerob^  longer 

Toni;::.!  .Lt.  i'*  u.  *»  ^ »« -.'..  -^  - 

Bets  a  little  to  the  west  of  it. 


% '- rl 


1- 


NORTH 
Fio.  4. 

«nm,  ♦«','^„'t^^  tSrfLTtoS  but  they  J« 
p,^t  MvotaUon  m  1^  "^^  jirtiac  from  «ch 
Swerve  iiiidi»nged  Aeir  """"^j,  ^„^  «,  wm- 
Uher,  tKth  the  «"»!*■<»>  ««  *7' '£?S  are  »WHe 

»chMg.  •ir.'JrJ  the  Se"''  the  ide.  thrt  thM. 
UrSttjrSrjTc^-neSl^^"-'^'--    ^ 


«rW".-flt. 


14 


ASTBONOMY. 


apparent  explanation,  both  of  this  and  of  the  phenomena 
of  the  diurnal  motion,  was  offered  by  the  conception  of 
the    celestial  sphere.      The    salient   phenomena   of  the 
heavens,  from  whatever  point  of  the  earth's  surface  they 
might  be  viewed,  were  represented  by  supposing  that  the 
globe  of  the  earth  was  situated  centrally  within  an  im- 
mensely larger  hollow  sphere  of  the  heavens.     The  vis- 
ible portion,  or  upper  half  of  this  hollow  sphere,  as  seen 
from  any  point,  constituted  the  celestial  vault,  and  the 
whole  sphere,  with  the  stars  which  studded  it,  was  called 
the  firmament.     The  stars  were  set  in  its  interior  surface, 
or  the  firmament  might  be  supposed  to  be  of  a  perfectly 
transparent  crystal,  and  the  stars  might  be  situated  in  any 
portion  of  its  thickness.     About  one  half  of  the  sphere 
could  be  seen  from  any  point  of  the  earth's  surface,  the 
view  of  the  other  half  being  necessarily  evt  off  by  the 
earth  itself.     This  sphere  was  conceived  to  make  a  diurnal 
revolution  around  an  axis,  necessarily  a  purely  mathemat- 
ical line,  passing  centrally  through  it  and  through  the 
earth.     The  ends  of  this  axis  were  the  poles.    The  situa- 
tion of  the  north  end,  or  north  pole,  was  visible  in  north- 
em  latitudes,  while  the  south  pole  was  invisible,  being 
below  the  horizon.     A  navigator  sailing  south  would  so 
change  his  horizon,  owing  to  the  sphericity  of  the  earth, 
that  the  location  of  the  north  pole  would  sink  out  of  sight, 
while  that  of  the  south  pole  would  come  into  view. 

It  was  clearly  seen,  even  by  the  r'  Jents,  that  the  diur- 
nal motion  could  be  as  well  represented  by  supposing  the 
celestial  sphere  to  be  at  rest,  and  the  earth  to  ravolve 
around  this  axis,  as  by  supposing  the  sphere  to  revolve. 
This  doctrine  of  the  earth's  rotation  was  maintained  by 
several  of  the  ancient  astronomers,  notably  by  Abistab- 
oHus  and  Timoohabis.  The  opposite  view,  however,  was 
maintained  by  Ptolbmt,  who  could  not  con<»ive  that  the 
earth  could  be  endowed  with  such  a  rapid  rotation  with- 
out disturbing  the  motion  of  bodies  at  its  surface^  We 
now  know  that  Ptolbict  was  wrong,  and  his  opponents  < 


THE  CELESTIAL  SPHERB. 


15 


phenomena 
mception  of 
lena  of  the 
surface  they 
ing  that  the 
thin  an  ira- 
B.  The  vis- 
lere,  as  seen 
alt,  and  the 
,  was  called 
rior  surface, 
a  perfectly 
lated  in  any 

the  sphere 
surface,  the 

off  by  the 
ke  a  diurnal 
'  mathemat- 
hrongh  the 

The  sitna- 
le  in  north- 
dble,  being 
h  would  so 

the  earth, 
tut  of  sight, 
idew. 

It  the  diur- 
pposing  the 
to  revolve 
to  revolve, 
intoined  by 
y  Abistab* 
>wev^r,  was 
!ve  that  the 
sation  with- 
pface*    We 

opponents  < 


right.  Still,  so  far  as  the  apparent  dinmal  motion  is  con- 
oerncd,  it  is  indifferent  whether  we  conceive  the  earth  or 
the  heavens  to  be  in  motion.  Sometimes  the  one  concep- 
tion, and  sometimes  the  other,  will  make  the  phenomenA 
the  more  clear.  As  a  matter  of  fact,  astronomers  speak 
of  the  sun  rising  and  setting,  just  as  others  do,  although 
it  is  in  reality  the  earth  which  turns.  This  is  a  form  of 
language  which,  being  designed  only  to  represent  the  ap- 
pearances, need  not  lead  us  into  error.  .^  ^  ,      , 

The  celestial  sphere  which  we  have  described  has  long 
ceased  to  figure  in  wrtronomy  as  a  reaUty.    We  now  know 
that  the  celestial  spaces  are  pmcticaUy  perfectly  void ; 
that  some  of  the  heavenly  bodies,  which  appear  to  l^  on 
the  surface  of  the  oelertial  sphere  at  equM  dwtaneesfrom 
the  earth  as  a  centre,  are  thousands,  or  even  milhons  of 
times  farther  from  the  earth  than  others ;  that  there  is  no 
material  oonneetion  betwefen  them,  and  that  the  celestial 
sphere  itself  ii»  only  a  result  of  optical  pewotive.    But 
the  huiguage  and  the  conception  are  stiU  ret&i»4^  1»cause 
they  afford  the  most  dear  and  definite  method  of  repre- 
sentimr  the  directioBs  of  the  heavenly  bodies  fiom  the 
obs«rw,  wherever  he  may  be  situated.    In  this  respect 
it  sema  the  same  pwpose  that  the  geometnc  sphere 
does  in  apherical  trigono^netry.    The  stodeiit  of  this  sci- 
ence knows  that  there  is  reaUyno  need  of  supposing  a 
sphere  or  a  spherical  trianj^e,  because  every  spherical  are 
is  only  the  representative  of  an  angle  between  two  lines 
which  emanate  from  the  centre,  one  to  each  end  of  the 
are,  whae  the  angles  of  the  triangle  are  only  those  of  the 
philies   containing  the   three  lines  which  are  drawn  to 
Lh  angle  from  the  centre.     Spherical  trigonometry  m, 
therefore,    in   reaMty,    only  the  trigonometry  oi   s^id 
angles ;  and  the  purpose  of  the  sphere  is  only  to  afford  a 
convenient  method  of  conceiving  of  such  angles.    In  the 
same  way,  althou^  the  celestial  sphere  has  no  real  ex- 
istence, yet  by  eonoeiving  of  it  a.  a  redity,  and  suppojng 
eertain  Unes  of  reference  drawn  upon  it,  we  are  enabled  to 


JWga»JM»»<i«!4i.!l,ttM!'.-'.'"?J?,^'t>'"''^.'fl 


16 


# 


A8TR0N0MT. 


form  an  idea  of  tlie  relative  directions  of  the  heavenly 
bodies.  We  may  conceive  of  it  in  two  ways  :  firetly,  as 
having  an  infinite  radius,  in  which  case  the  centre  of  the 
earth,  or  any  point  of  its  surface,  may  equally  be  supposed 
to  be  in  the  centre  of  the  celestial  sphere ;  or,  secondly  we 
may  suppose  it  to  be  finite,  the  observer  carrying  the  wn- 


Fio,  5 — aTARs  nam  oir  thk  CBuniAi.  vbmhm. 


tre  with  him  wherever  he  goes.  The  iirat  assumption  wiU 
probably  l)e  the  one  which  it  is  best  to  adopt.  The  object 
attained  by  each  mode  of  representation  is  that  of  having 
the  observer  always  in  the  centre  of  the  supposed  sphere. 
J*^.  5  will  give  the  reader  an  idea  of  its  apphcatjon.  He 
w  supposed  to  be  stationed  in  the  centre,  0,  ancl  to  have 
Mwmd  him  the  bodies py».,<,  etc  The  sphere  itself 
temg  supposed  at  an  immense  distance,  outside  of  all 
these  bodies,  we  may  suppose  lines  to  be  drown  fiom 
each  of  them  directly  away  from  the  centre  until  they 
waoh  the  sphere.     The  points  PQBST,  etc.,  in  whieh 


=s& 


■i-.i  j*w<wiiw.jMiji|iiiwm 


^ 


the  heavenly 
1^8  :  firstly,  as 
centre  of  the 
r  be  supposed 
secondly,  we 
jring  the  oen- 


imptifMi  will 
liie  object 
it  of  having 
Bed  sphere. 
Mtlon.  He 
um)  to  have 
phere  itself 
»ide  of  all 
rawn  itom 
until  they 
!.,  in  -wladi 


THE  CELESTIAL  SPHERE. 


17 


these  lines  intersect  the  sphere,  will  represent  the  appa- 
rent positions  of  the  heavenly  bodies  as  seen  by  the  ob- 
server at  0.  If  several  of  them,  as  those  marked  ttt^ 
are  in  the  same  direction  from  the  observer,  they  will  ap- 
pear to  be  projected  on  the  same  point  of  the  sphere. 
Thus  positions  on  the  sphere  represent  simply  the  direc- 
tions in  which  the  bodies  are  seen,  bnt  have  no  direct  re- 
lations to  the  distance. 

It  was  seen  by  the  ancients  that  the  earth  was  cmly  a 
point  in  comparison  with  the  appfrent  B|dtoi«  of  the  fixed 
stars.  This  was  shown  by  the  nniformity  of  the  dinmal 
motion ;  if  the  earth  had  any  sensible  magnitnde  in  com- 
parison with  the  sphere  of  the  heavens,  the  son,  or  a  star, 
would  seem  to  be  nearer  to  the  observer  when  it  passed 
the  meridian,  or  any  point  near  his  zenith,  than  it  wotild 
when  it  was  below  the  horizon,  or  nearly  under  his  feet, 
by  a  quantity  equal  to  the  diameter  of  the  earth.  Being 
nearer  to  him,  it  would  seem  to  move  more  rapidly  when 
above  the  horizon  than  when  below,-  and  its  apparent  angular 
dimensions  would  be  greater  in  the  zenith  than  in  the 
horizon.  4s  a  matter  of  fact,  however,  the  most  refined 
observations  do  not  show  tlie  slightest  variation  from 
perfect  uniformity,  no  matter  what  the  point  at  which 
the  observer  may  stand.  Therefore,  observers  all  over 
the  earth  are  apparently  equally  near  the  stars  at  every 
point  of  their  apparent  diurnal  paths;  wbence  their 
distance  must  be  so  great  that  in  proportion  to  them  the 
diameter  of  the  earth  entirely  vanishes.  This  aigoment 
holds  equally  true  whether  we  suppose  the  earth  or  tiie 
heavens  to  revolvis,  because  the  observer,  carried  around 
by  tlie  rotating  earth,  will  be  brought  nearer  to  those 
stars  which  are  over  his  head,  and  carried  farther  from 
them  when  he  is  on  the  opposite  side  of  the  circre*in 
which  he  moves. 

« 

Bajqxwe  tht  earth  to  be  at  0,  and  the  celestial  sphere  of  the  fixed 
■taiato  be  represent^  in  the  figure  by  the  circle  NZ  QSn,  etc. 
BuppoM  N  E8  W  to  reprewnt  the  plane  of  the  hrriton  of  aome 


18 


A8TR0N0MT. 


obwrrer  on  the  ewth*s  ■urfaoe. 


He  will  then  aee  every  thing  oSmm 
thie  plane,  and  nothbg  befow  it 
If  NB  8  it  hit  etutem  horizon, 
■tan  will  •Ppear  to  rise  atTarioiu 
points,  g,  E,  d,  a,  etc.,  and  will 
appear  to  describe,  circles  until 
they  attain  their  highest  points 
at  A,  Q,  0,  h,  etc.,  dnking  into 
the  western  horizon  at  t,  W,  /,  «, 
etc.  These  are  facts  of  observa- 
tion. The  common  aaiU  of  tliose 
circles  is  P  ^,  and  stars  about  P 
(the  pole)  never  set.  The  appa- 
rent diurnal  arc  I  m,  for  icatance, 
represents  the  apparent  wbit  of 
a  eirmmpolor  star. 


ViQ.  9. 


THS   TSBBB8TBIAL 


8.  OOBBBSPOHDBNCB   OF 
AND    OXIiBSTIAL 


We  have  said  that  the  direction  of  a  heavenly  body 
from  an  observer,  or,  which  is  the  same  tiling,  its  ap- 
^parent  position,  is  defined  by  the  point  of  the  celestial 
sphere  on  which  it  seems  to  be.  This  point  is  that  in 
which  the  straight  line  drawn  from  the  observer  to  the 
body,  and  continued  forward  indefinitdy,  meets  the  celes- 
tial sphere.  Its  position  is  fixed  by  reference  to  certain 
fondamental  circles  supposed  to  be  drawn  on  tiie  sphere, 
on  the  same  plan  by  which  longitude  and  latitude  on  the 
earth  are  fixed.  The  system  of  thus  defining  terrestrial 
positions  by  reference  to  the  earth's  equator,  and  to  some, 
prime  meridian  &om  which  we  reckon  the  longitudes,  is  one 
with  whidi  the  reader  may  be  supposed  familiar.  We  shall 
therefore  commence  with  those  eireles  of  the  celestial 
sphere  which  correspond  to  the  meridians,  parallels,  etc, 
onlthe  earth. 

First,  we  remark  that  if  we  consider  the  earth  to  be  at 
rest  for  a  moment,  every  point  on  its  surface  is  at  the  end 
of  a  radius  which,  if  extended,  would  toneh  a  correspond'- 


..jimmianii 


IWiaailBillBjBWM'IWIIWWIIili 


m  thing  dboM 
;huig  bflfow  it 
Mttem  horizon, 
(riaeatTuioaa 

etc.,  and  will 
«  circles  until 
hiffheet  points 
,  nnking  into 
nat*,  r,/,  e, 
cts  of  obsenra- 
o  aada  of  these 

stars  about  P 
t.  The  appa- 
I,  for  instance, 
•rant  orbit  of 


EtBffFBIAL 


ivenly  body 
ling,  its  ap- 
the  celestial 
It  is  that  in 
erverto  the 
)tB  the  oeles- 
«  to  certain 
the  sphere, 
itnde  on  the 
g  terrestrial 
and  to  some 
itddes,  is  one 
v.  We  shall 
the  celestial 
rallels,  etc, 

rth  to  beat 
•  at  the  end 
oorrespondo 


TBt  OBLESTIAL  AND  TtBHtSTUAL  BPBlBiSI.    W 
,„g  point  «pon  A.  ctatW  •^J\^^":X 

the  MUth  in  dediied  by  »  bm  P~'"*„ "  ;„  diraotlT  np- 
rf  the  e«th  to  th.  ol«r™r,  »d  r*'"';j«,^^JJS; 
,^  until  it  m«t.  th.  '»>»^'ifl*"r^^  wh^7h. 

''*^''' wLthe  oSTrverTon  «ie  eartVs  equator. 

^U  «ee  hi.  zenith »«« -•y^^^^^h'^m  d-criSi  a 
the  earih  revolve,  on  it.  «-» .^»  TT  every  point  of 
great  circle  around  tlu.  celestial  »P^«^  •^"Y^^  „  ^e 
^ch  wiU  be  eqniOly  dirtant  'TV^'fTm  „y ^t 

of  the  ewrth's  equator  ^e'^^Uj;*?  ^^  ^ '     them, 
conceive  ihai  iU  !»««*  «f  ^  ««*  jj  S^  irbadf  to  the 

called  the  «*•««  '''^'.^^TZIn^t^iT^  above  a 
to  the  terrestrial  eqnator  is  t\«*  ^J^'T^;"^;  "tors  lie 
corresponduM^  point  ofihela^The^two^^  ^^  ^^^ 

f^^'^^^tA^Sandtorr^  ^ 

belong,  to  both  *~  ?T^^     ^^  from  the  eqnator 

Now  .appow  that  the  ^^^^T^^Thavinir  changed  by 
to  460  of  north  latitude.  ^^^^""^^VX^SSon, 
45-,  the  noiih  polej^  now^be  46    *ove  ^^  ^^ 


imMm^L'^-.^W. 


80 


ASTRONOMY. 


sphere  which  Mrill  be  overywliere  45"  distant  from  the 
celestial  equator.  This  cirde  will  thus  correspond  to  the 
parallel  of  45°  north  upon  the  earth.  If  he  goes  to  lati- 
tude 60°  north,  he  will  see  the  pole  at  an  elevation  of  60°, 
and  his  zenith  will  in  the  same  way  describe  a  circle  which 
will  be  everywhere  60°  from  the  celestial  equator,  and  80° 
from  the  pole.  If  he  passes  to  the  polo,  the  latter  will 
be  directly  over  his  head,  and  his  zenith  will  not  move  at 


FlO.  7.— TBBBnTRUIi  AXD  (ntUWIAI. 


all.  The  celestial  pole  is  simply  the  point  inwiiioh  the 
earth's  axis  of  rotation,  if  continued  out  in  a  straight  line 
of  infinite  length,  would  meet  the  celestial  sphere.  We 
thus  have  a  series  of  circles  on  the  celestial  spliere  ooire- 
sponding  to  the  parallels  of  latitude  upon  the  eartk. 
Unfortunately  the  celestial  element  owresponding  to 
latitude  on  the  earth  is  not  called  by  that  name,  but  by 
that  of  dedmaUon.  The  d«dinaUon  of  a  tkax  is  ^ 
distance  north  or  south  from  the  edestial  equator,  pre- 


■■r 


»nt  from  the 
'espond  to  the 
goes  to  kti- 
ivation  of  60", 
a  circle  which 
aator,  and  80" 
he  latter  will 
1  not  move  at 


in  whioh  the 
a  straight  line 
sphere.  We 
splbere  oorre- 
n  the  earth. 
9ep<niding  to 
name,  bnt  by 
a  star  is  ^ 
eqiiator,  pre- 


and  J7  e  its  equator.     «  "  /"l"  ..^m^imshH^^^ 

the  VLw  LF  .^^f^rSrJ^  w  jp" 
finite  di«t»ce thedlitMiM r^  r 

the  elevted  pole.  correspondence  between 

We  have  next  to  consider  t^e  cwrespu^  terrestrial  me- 
the  celestial  and  ^^r\^^'Zfr  the  earth's  snrf ace 
ridian  is  ^  '^'^^'''^y^rSrotZ  pole  to  the  other, 
in  .  north  and  sonA  ^^"Z  pole  in  every  diiec- 
Thesemeridiansdijerge  from  one  F*  ^^y 

tion,  and  meet  at  the  o^erjok^    ^  through    «  the 
edled  by  A*  "'"^T.^J  ^Te  mlridSwi  of  Washington. 
,„eridian  of  ^^""^^^JZlllr^  as  the  intersection  witli 
E^  meridian  may  be  <^f '^  ^^^ongh  the  axis  of 
jre«rth'ssnrf«»ofaplajeT^«J^^   ^les.     Such  a 
Z  earth,  ««*  *«tS^„S^  e^l  hrnispherea,  «.d 
pl««,  will  cut  the  eaiAjntoJ^JJl^rth's  surface  Jong 
L-  \  of  oonne  be  vertical  y^V, "      This  phme  is  called 
V^^  of  its  li»-^^*?'::^^y  co?t.^^ng  it  2^  t« 
the  Jlaneof  the  «»«"*"? '^^ve  a  celestial  meridian 

Teloestial  sphere,  T'J^^J^Zl  precisely  as  we  have 
.      oorwspondinp  to  each  terrestrial  one,  p 


JS^Ef 


S^^l^yilK'lW'ii'e^'^^*-'^*^'^ 


m 


mi 


wm 


S8 


ASTJtomifr. 


circles  of  declination  corresponding  to  parallels  of  latitnde 
on  the  earth.     But  owing  to  the  rotation  of  the  earth,  the 
circle  in  which  the  plane  of  the  meridian  of  any  place  in- 
tersects the  celestial  sphere  will  be  continnally  moving 
among  the  stars,  so  that  there  is  no  such  permanent  cor- 
roapondence  as  in  the  case  of  the  declinations.     Thii 
does  not  prevent  us  from  conceiving  imaginary  meridiana 
pawing  from  one  pole  of  the  heavens  to  the  other  pre- 
cisely as  the  meridians  on  the  earth  do,  only  these  me- 
ridiang  will  be  apparently  in  motion,  owing  to  the  rotation 
of  the  earth.     We  may,  in  fact,  conceive  of  two  seta  of 
meridiana— one  really  at  rest  among  the  stars,  but  appa- 
rently moving  from  east  to  west  around  the  pole  as  the 
rtara  do,  and  the  other  the  terrestrial  meridians  continued 
to  the  celestial  sphere,  apparently  at  rest,  but  really  in 
inotion  from  west  to  east.     The  rektions  of  these  me- 
ridians will  be  best  understood  when  we  explain  the  in- 
strnmonts  and  methods  by  which  they  are  fixed,  and  by 
which  the  positions  of  the  stars  in  the  heavens  are  deter- 
mined.     At  present  we  will  confine  ourselves  to  the  con- 
sideration  of  the  celestial  meridians. 

The  reader  will  understand  that  these  meridians  pass 
from  one  pole  of  the  celestial  sphere  to  the  other,  pre- 
cisely as  on  the  globe  terrestrial  meridians  pass  from  one 
pole  to  the  other,  and  that  being  fixed  among  the  stars, 
they  appear  to  turn  around  the  imle  as  the  stars  appear  to 
do.  As  on  the  earth  differences  of  longitude  betwefo 
different  places  are  fixed  by  the  differences  between  the 
meridians  of  the  two  pkces,  so  in  the  heavens  what  eor- 
responds  to  longitude  is  fixed  by  the  differenoe  between 
the  celestial  meridians.  This  coordinate  is,  however,  in 
the  heavens  not  caUed  longitude,  but  righi  Moeruion, 
Let  the  student  very  thoroughly  impres»  upon  his  mind 
this  term— right  ascension— which  k  ^Itngitnde  on  the 
celestial  sphere,  and  also  the  tenu  i^riiavefbefore  spoken 
of— (JM^MMi^Mm— whieh  u  latitude  on  the  celestial  sphere. 

In  order  to  fix  the  right  ascension  of  a  hea^««ly  bodyj 


\hU  of  latitude 
the  earth,  the 
any  pjgce  in. 
inally  moving 
)nnanent  oor- 
lations.     Thig 
larjr  ineridiana 
he  other  pre- 
Inly  these  me- 
» the  rotation 
f  two  aeta  of 
"*>  but  appa. 
)  pole  as  the 
ana  oontinaed 
hut  really  in 
of  these  rae- 
fphiin  the  in- 
<ixed,  and  by 
ens  are  deter- 
*8  to  the  con- 

fierjdiana  pass 
le  other,  pi«. 
MB  from  one 
*>fir  the  Stan, 
*«  appear  to 
ade  between 
between  the 
>n8  what  ow. 
nee  between 
however,  in 

^  MMfWMn,     , 

n  his  mind 
ude  on  the 
f<n«  spoken 
itialsphflve. 
^••ly  body, 


niGirr  ah(irnsion. 


88 


we  must  liave  a  first  meridian  to  count  from,  precisely  as 
on  the  earth  we  count  longitudes  ^rom  the  meridian  of 
Greenwich  or  of  Washington.  L*  'ndiilerent  wliat  me- 
ridian we  take  as  the  first  one  ;  uat  it  is  custouiary  to 
adopt  the  meridian  of  the  vernal  equinox.  What  the  ver- 
nal ef^uinox  is  will  lie  described  hereafter :  for  our  pres- 
ent purposes,  nothing  more  is  necessary  than  to  under- 
stand that  a  certain  meridian  is  arbitrarily  taken.  If  noM' 
we  wish  to  fix  the  right  ascension  o^  a  star,  we  have  only 
to  imagine  a  meridian  passing  through  it,  and  to  deter- 
mine the  angle  which  this  meridian  makes  with  the  meri- 
dian of  the  vernal  equinox,  as  measured  from  west  to  east 
on  the  equator.  That  angle  will  be  the  right  ascension  of 
a  star.  As  already  indicated,  the  declination  of  a  star 
will  be  its  angular  distance  from  the  equator  measured  on 
this  meridian.  Thus,  the  right  ascension  and  declination 
of  a  star  fix  its  apparent  position  on  the  celestial  sphere, 
precisely  as  latitude  and  longitude  fix  the  position  of  a 
point  on  tlie  surface  of  the  jsarth. 

To  give  precision  to  the  ideas,  we  present  a  brief  con- 
densation of  this  snbjeet,  with  additional  definitimis. 

Let  PZ^iT represent  the  oeleetial  sphere  of  on  ob- 
server  in  the  northern  hemisphere,  O  being  the  position 
of  the  earth.  Pp  is  the  oanaqf  ike  odesHal  tphere^  or 
the  line  about  whieh  the  appwent  dinmal  orbits  of  the 
stars  and  the  actual  revolution  of  the  earth  are  performed. 

The  zenith,  Z,  is  the  point  immediately  above,  the 
nadir  n,  the  point  immediately  below  the  observer. 
The  direction  Zn  is  defined  in  practice  by  the  position 
freely  assumed  by  the  plnmb  line. 

The  celettial  Kmnzon  is  the  plane  perpendicular  to  the 
line  jc^ng  the  aenHA  and  nadir  IfES  W;  or  it  is  the 
terrestrial  horiion  ocmtinued  till  it  meets  the  oeleetial  sphere. 

The  cdestial  horiaon  intersects  the  earth  in  the  rational 
AdfuwM,  whieh  pasaes  through  the  earth's  centre,  and 
whidi  ia  so  called  in  distinction  to  the  mmKe  horiion^ 
whieh  ia  the  plane  tangent  to  the  earth's  surface  at  any 


mg^: 


14  ASTHoyoMY. 

point.  But,  since  the  earth  itself  is  considered  as  but  » 
point  in  comparison  witli  tlie  celestial  sphere,  the  rational 
and  sensible  horizons  mo  considered  as  one  and  the  same 

circle  on  this  sphere.  .      -  .1 

The  oelettial  poUm  are  the  extremities  of  the  (wis  of  m 
ededial  sphere  P  p,  the  nwth  poU  l«ing  that  one  which 
is  above  the  horizon  in  the  latitude  of  New  \ork,  in  the 

northern  hemisphere.  ,  .      ,       .       •*!.«- 

The  circles  apparently  described  by  the  stars  m  their 

diurnal  orbits  are  called  ptmMtU  qf  dedwatwn,  KN ; 


Fie.  0.— cnoun  ov 


that  one  whose  plane  passes  through  the  centre  of  the 
sphere  being  the  «fo««»a/  eqwOWy  or  the  tfumoaUalf 

C  W  D. 

The  odeKliaSL  tfuatar  is  then  that  pundlel  of  declination 
which  is  a  great  drole  of  the  celestial  sphere. 

The  figure  iUustawtes  the  phenomena  which  appear  in 
the  heavens  to  an  observer  upon  the  earth.  The  stan 
which  Ue  in  the  equator  have  their  diurnal  paths  bisected 
by  the  horizon,  and  are  as  long  above  the  horiaon  as  b«l»W 


>nsidored  as  but  a 
[pliere,  tho  rational 
one  and  the  same 

of  the  ojtls  of  the 

^ing  that  one  which 

New  York,  in  tho 

the  Stan  in  their 
\dedinatumy  KN ; 


\  the  centre  of  the 
or  the  tqmiMalMly 

andlel  of  dedination 

■phere. 

nut  which  appeMr  in 

te  earth.    Th«  itan 

innud  patiha  bJMdted 

the  horiion  as  helaw 


'^ 


VIHCim  OF  TUi  1 1  Kit  K.  • 

it ;  tho8<t  who8u  diHtancu§  from  tho  \mAo  {fnd<fr-'/ii*f" 
are  gn>uter  than  90°  will  bu  a  Hliurtur  tiniu  nbuv«'  tlit 
rizon  ;   those  whoso  polar-distance*  aru  lues  than  i**     li 
longer  time. 

Tho  circle  iViT drawn  aronnd  tho  pole  Pm  a  centre 
fo  as  to  graze  the  horizon  is  called  the  circle  iif  perpetual 
apparition^  liecauso  stars  situatKl  within  it  never  set. 
The  corresponding  circle  S  U  round  tho  south  polo  is 
called  tho  circle  qfperpetvMl  disappearance,  because  stars 
within  it  never  rise  above  our  horizon. 

The  groat  circle  passing  throu«di  the  zenith  and  the 
pole  is  the  celettial  meridian,  NPZS.  The  meridian 
intersects  the  Korixon  in  the  meridian  line,  and  the  points 
N and  8 are  the  north  and  touthpointg. 

the  prime  vertical,  £ZW,i»  perpendicular  to  the  meri- 
dian line  and  to  the  horizon :  its  extremities  in  the  hori- 
zon are  the  ead  and  toettpointt. 

The  meridian  plane  is  perpendienlar  to  the  equator  and 
to  the  horizon,  and  therefore  to  their  inteiMction.  Hence 
this  intersection  it  the  eatt  and  VMti  line,  which  ia  thus 
determined  by  the  inteneotion  of  the  ]danei  of  the  equator 
and  of  the  hn-imm. 

The  edUtudt  of  a  htwrenly  body  ia  ita  apparent  distance 
above  the  horison,  expreaaed  in  degreea,  minutes,  and 
seconds  of  aro.  hk  the  cenith  the  altitude  is  90**,  which 
is  the  greatest  poarible  attitude. 

If  ^  be  any  hetTenly  body,  tho  angle  ZPA  which  the 
oirde  P  A  drawn  from  the  pole  to  the  body  makes  with 
the  meridian  ia  ealled  the  hour  angle  of  the  body.  The 
hour  angle  ia  the  angle  through  which  the  earth  has  ro- 
tated on  ita  axis  aince  the  body  was  on  the  meridian.  It 
is  ao  called  becauae  it  measurea  the  time  which  has 
elapaed  linoe  the  paange  of  the  body  over  the  meri- 
dian. 

Thai  diameter  of  the  earth  which  ia  coincident  with  the 
Qonataat  diraotion  of  the  axis  of  the  oekacial  aphere  is  its 
MM,  and  interaeots  the  earth  in  ita  north  and  aouM  poUz, 


<t-<i^''-wagggj." 


W^ 


2rt 


AHTUONOMY. 


JOrWMBMKT  LATI* 


K  4.  THl  DXUBir  AL  MOTION  IN 
■  TUDE8. 

As  wo  have  ueon,  ih  celestial  horizon  of  an  observer 
will  change  ita  place  on  the  celestial  sphere  as  the  observer 
travels  from  place  to  place  ou  the  sarfaco  of  the  earth. 
If  he  moves  directly  toward  the  north  his  zenith  ^rill  ii|>- 
proach  tho  north  polo,  but  as  the  zenith  is  not  a  visible 
point,  the  motion  will  be  naturally  attributed  to  the  pole, 
which  will  seem  to  approach  the  point  overhead.  The 
new  apparent  position  of  the  pole  will  change  the  aspect 
of  the  observer's  sky,  as  the  higher  the  pole  appears  above 
the  horizon  the  greater  the  circle  of  perpetual  apparition, 
and  tlterefore  the  gi-eater  the  number  of  stars,  wliich 
never  set. 


If  the  observer  is  at  the  north  pole  his  zenith  and  the 
pole  itself  will  coincide  :  half  of  the  stars  only  will  be  vis- 
ible, and  these  will  never  rise  or  set,  but  appear  to  nwve 
around  in  circles  parallel  to  the  horizon.  .  The  horijcon 
and  equator  will  coincide.  The  meridian  will  be  indetw- 
minate  since  Z  and  P  coincide ;  there  will  be  no  eMt  and 
west  line,  and  no  direction  but  south.  The  sphere  in  this 
case  is  called  a  paraUd  tphere. 


WMSLMKT  UlTI- 

1  of  an  observer 
V  an  the  observer 
iuo  of  the  earth, 
lia  zenith  '^11  )i|)- 

is  not  a  visible 
voted  to  the  pole, 

overhead.  The 
change  the  aspect 
ole  appears  above 
)etnal  apparition, 

of  stars,  wliich 


is  zenith  and  the 
rs  only  will  be  vis- 
it appear  to  move 
aa.  .  The  horicon 
an  will  be  indetw- 
will  b«  DO  eaat  and 
The  sphere  in  this 


'.''■S8'":V 


DIUHNAL  MOTION  IN  DIFFKHKNT  LATITUDISS.    97 

If  itiHtuud  of  tnivt'Uiiig  to  the  nortli  the  oltnerver  shuiild 
go  toward  tiie  (Hiuatoi*,  the  nortli  pole  woiUd  seem  to  ap- 
proach iiiH  horizon.  Vt'hon  he  reached  the  (Hjuator  Itoth 
poles  would  be  in  the  horizon,  one  north  and  the  other 
Honth.  All  the  Btiirs  in  buccetwion  would  then  be  viHible, 
and  each  would  bo  an  equal  time  above  and  below  the 
horizon. 


Fm.  11 


The  sphere  in  this  case  is  called  a  righi  (^here,  because 
the  diurnal  motion  is  at  right  angles  to  the  horizon.  If  now 
the  observer  travels  southward  from  the  equator,  the  south 
pole  will  become  elevated  above  his  horizon,  and  in  the 
southern  hemisphere  appearances  will  be  reproduced 
whidi  we  have  idready  described  for  the  northern,  except 
that  the  direction  of  the  motion  will,  in  one  respect,  be 
di£Ferent.  The  heavenly  bodies  will  still  rise  in  tie  east 
and  set  in  the  west,  but  those  near  the  equator  will  pass 
north  of  the  zenith  instead  of  south  of  it,  as  in  our  lati- 
tudes. The  sun,  instead  of  moving  from  left  to  right, 
tliera  moves  from  right  to  left.  The  bounding  line  be- 
tween the  two  directions  of  motion  is  the  equator,  where 
the  snn  culminates  north  of  the  zenith  from  Haroh  till 
September,  and  south  of  it  from  September  till  March. 

If  the  observer  travels  west  or  east  of  hb  first  sta- 
tic, his  lenith  will  still  remain  at  the  same  angular 


28 


ASTRONOMY. 


distance  from  the  north  pole  as  before,  and  as  the  phe- 
nomena caused  by  the  earth's  diurnal  motion  at  any 
place  depend  only  upon  the  altitude  of  the  elevated  pole 
at  that  place,  these  will  not  be  changed  except  as  to  the 
times  of  their  occurrence.  A  star  which  appears  to  pass 
through  the  zenith  of  his  first  station  will  also  appear  to 
pass  through  the  zenith  of  the  second  (since  each  star  re- 
mains at  a  constant  angular  distance  from  the  pole),  but 
later  in  time,  since  it  has  to  pass  through  the  zenith  of 
every  place  between  the  two  stations.  The  horizons  of 
the  two  stations  will  intercept  difiEerent  portions  of  the 
celestial  sphere  at  any  one  instant,  but  the  earth's  rotation 
will  present  the  same  portions  successively,  and  in  the 
same  order,  at  both. 

§  6.  BEI.ATI01T  OF  TIME  TO  THB  8FHEBB. 

As  in  daily  life  we  measure  time  aj  the  revolution  of 
the  hands  of  a  clock,  so,  in  astronomy,  we  measure  it  by 
the  rotation  of  the  earth,  or  the  apparent  revolution  of 
thf  celestial  sphere.  Since  the  sphere  seems  to  perform 
one  revolution,  or  360°  in  24  hours,  it  follows  that  it 
moves  through  16"  in  one  hour,  1°  in  4  minutes,  16'  in 
one  minute  of  time,  and  16*  in  one  second  of  time. 

The  hour  angle  of  a  heavenly  body  counted  toward  the 
west  (see  definition,  p.  26)  being  the  angle  tlirough  which 
the  sphere  has  revolved  since  the  passage  of  the  body  over 
the  meridian,  it  follows  that  the  time  whidi  has  elapsed 
eince  that  passage  may  be  fonnd  by  dividing  the  hour 
angle,  expressed  in  degrees,  minutes,  and  seconds  of  arc, 
by  15,  when  the  result  will  be  the  required  interv^  ex- 
pressed in  hours,  minutes,  and  seconds  of  timo.  If  we 
know  the  time  at  which  the  body  passed  the  meridian, 
and  add  this  interval  to  it,  we  sludl  have  the  time  corre- 
sponding to  the  hoar  angle.  If  we  call  it  noon  when 
the  sun  passes  the  meridian,  the  hoar  angle  of  the  son 
at  any  moment,  divided  by  16,  gives  the  time  since  noon. 
Me<m  aolar  time  h  onr  ordinary  time  measured  by  the 


SIDEREAL  TIME. 


39 


i  as  the  phe- 
lotion  at  any 
elevated  pole 
3ept  as  to  thci 
>pear8  to  pass 
ilso  appear  to 
each  star  re- 
the  pole),  but 
the  zenith  of 
e  horizons  of 
)rtion8  of  the 
arth's  rotation 
y,  and  in  the 

8FHEBE. 

I  revolution  of 
measnre  it  by 

revolution  of 
ns  to  perform 
ollows  that  it 
ninutes,  15'  in 
>f  time. 

ted  toward  the 
tlirough  whidi 

the  body  over 
'Ja  has  elapsed 
ling  the  hour 
leconds  of  arc, 
id  interval  ez- 

timo.  If  we 
the  meridian, 
he  time  cone- 
it  noon  when 
^le  of  the  sun 
me  since  noon, 
lasnred  by  the 


«un,  after  allowing  for  certain  inequalities  hereafter  de- 

"1£re,  however,  an  important  remark  is  to  be  made^ 
Really  ihe  earth  does  not  revolve  on  its  axis  m  24  of  he 
^ZnZ  in  ordinary  life,  but  in  about  4  minutes  less  than 
^hirclre  exactly  in  23  hours  56  minutes  4.09  seconds  ) 

If  wei^te  the  exact  time  at  which  a  star  crosses  the  men- 

i irorri-or  setB,  ordisappearsbehmd  achunney  or  o^^^^ 

terr^trial  object  on  one  night,  we  shall  find  it  to  do  tue 

rXTnaS  minutes  56  seconds  earlier  on  the  night  follow- 

thet^^ween  two  tr«»i..  of  the  «.n  o^  «»  »- 
V.       I.  *  K„  ♦!,«♦  between  two  transits  of  tne  same  siar. 

rfter  d.«ned),  mi  »  .bout  8  'r""f',"XdMded  into 

r^r:-:s*^^-^brcwideai.to 

24  tuureat  nourvj  ««*  „.a«tiv  like   the  common 

JlTrate- that  is,  it  gains  about  one  second  m  sixminutes, 


30 


ASTRONOMT. 


ten  seconds  in  an  hour,  3  minutes  56  seconds  in  a  day, 
two  hours  in  a  month,  and  24  hours,  or  one  day,  in  a  year. 
The  hours  of  the  sidereal  day  are  counted  forward  from  0 
to  24,  instead  of  being  divided  into  two  groups  of  12  each, 
as  in  our  civil  reckoning  of  time.  The  face  of  the  sidereal 
clock  is  divided  into  24  hours,  and  the  hour  hand 
makes  one  revolution  in  this  period  instead  of  two.  The 
minutes  and  seconds  are  each  counted  forward  from  0  to 
60,  as  in  the  common  dock.  Tho  hands  are  set  so  as  to 
mark  O*"  0"  0»  at  the  moment  when  the  vernal  equinox 
passes  the  meridian  of  the  observer.  Thus,  the  sidereal 
time  at  any  moment  is  simply  the  interval  in  hours,  min- 
utes, and  seconds  which  has  elapsed  since  the  vernal  equi- 
nox was  on  the  meridian.  By  multiplying  this  time  by 
16,  we  have  the  number  of  degrees,  minutes,  and  seconds 
through  which  the  earth  has  turned  since  the  transit  of 
the  vernal  equinox. 

The  sidereal  time  of  onr  common  noon  is  given  in  the 
astronomical  ephemeris  for  every  day  of  the  year.  It  can 
be  found  within  ton  or  twelve  minutes  at  any  time  by  re- 
membenng  that  on  March  22d  it  is  sidereal  0  hours  about 
noon,  on  April  22d  it  is  about  2  honro  sidereal  time  at 
noon,  and  so  on  through  the  year.  Thus,  by  adding  two 
hours  for  each  month,  and  4  minutes  for  each  day  after 
the  22d  day  last  preceding,  we  have  the  sidereal  time  at 
the  noon  we  require.  Adding  to  it  the  number  of  hours 
since  noon,  and  one  minute  more  for  ever  fourth  of  a  day 
on  account  of  the  constant  gain  of  the  clock,  we  have  the 
sidereal  time  at  any  moment. 

Eeam/ple. — Find  the  sidereal  time  on  July  4th,  1881,  at 
4  o'clock  A.1I.     We  have :  i 

h  ■ 
June  22d,  3  months  after  March  22d ;  tobe  X  S,  6  0 
July  3d,  12  days  after  June  22d ;  x  4,  0  48 

4  A.M.,  16  hours  after  noon,  nearly  |  of  a  day,       16     3 


This  result  is  within  a  minute  of  the  truth. 


22  51 


8IDSBBAL  TIME. 


81 


ids  in  a  day, 
iay,  in  a  year, 
orward  from  0 
pe  of  12  each, 
)f  the  sidereal 
e  hour  hand 
of  two.  The 
ard  from  0  to 
e  set  so  as  to 
emal  equinox 
},  the  sidereal 
n  hours,  min- 
e  vernal  equi- 
this  time  by 
},  and  seconds 
the  transit  of 

1  given  in  the 
year.  It  can 
y  time  by  re- 
)  hours  about 
ereai  time  at 
J  adding  two 
ush  day  after 
iereal  time  at 
iberof  hours 
nrth  of  a  day 
we  have  the 

4th,  1881,  at 

h       ■ 

X  S,    6     0 
0  48 

r,     16    8 

22  61 


Th«  reader  now  understands  that  a  sidereal  dock  is  one 

the  Bun,  but  by  ttat  of  'f  f^.  J^",,^  ,  ki„„  the 

'""TroX':^'*«WvX  ^t'nSL    We  h.ve 
poBtiont  of  the  rt«re  ^«^     J  ;„„  „i  ,ho  rtars 

now  to  .how  how  he  fin^  the  ng^  ^^  ^^  ___^_.. 

S'jr^nl^e.t.^f  *i-  ^-i.'-- «^-^ 

for  the  chapter  on  »»^'"«™-    "       .  j„^  j,  a^ed  in  an 
a  ™aU  ttleaeop;  ""^J*  «^  ^  !»  «xed,  the  tele- 

power  of  the  tele«.pe.    ^*  ".Srir^acay  on  the 

»r'rs;te'rr^"^''--a^. 

Suppose  now  in  ^^  ^^  ^^^^  moment 

mmBm 

'''''^X!^tfi^t^r^^^»^^<>-  of  «.y  rtar  or 
again.    Then,  *p^'***^™    *,        y^enit  ig  about  to  reach 

other  heavenly  ^y»^l^*^f,!i^t  instrument  at  the 
the  meridian ;  then  directo  the  *«,""*  ^^"^^  time, 
point  where  it  is  about  to  cross,  and  notes  ^  eMCt^ 

Shouts,  minutes,  and  •^"^•;;r^J*'^^ti7yi^ 

"^^  tt  te^'haft  :4m  ^.^n  of^'^r^  de- 
time  by  16,  he  has  tne  ngni  'T;  ,    ^^      j^  the  trouble 

SS.t^^oH'^n.w^lXtoex^i^. 


|ij,uj;ii.,i 


'I   I  ii.|ii|i 


82 


ASTRONOMY. 


riglit  ascensions  of  tlie  heavenly  bodies,  not  in  degrees, 
but  in  time.  The  circle  is  divided  into  24  houre,  like 
the  day,  and  these  hours  are  divided  into  minutes  and 
seconds  in  the  usual  way.  Then  the  right  ascension  of 
a  star  is  the  same  as  the  sidereal  time  at  which  it  passes 
tlie  meridian. 

The  relation  of  arc  to  time,  as  angular  measores,  can  be 
readily  remembered  by  noting  that  a  minute  or  a  second 
of  time  is  fifteen  times  as  great  as  the  corresponding  de- 
nomination in  arc,  while  the  hour  is  15  times  the  degree. 
The  minute  and  second  of  time  are  denoted  by  the  initial 
letter  of  their  names.     So  we  have : 


1"  =16" 
1"=16' 
1*=15' 


1"'=4» 

l'=4» 

1"=0'.0666. 


Belation  of  Time  and  Longltade.— Considering  our  civil 
time  as  depending  on  the  sun,  it  will  be  seen  that  it  is 
noon  at  any  and  every  place  on  the  earth  when  the  son 
crosses  the  meridian  of  that  place,  or,  to  speak  with  more 
precision,  when  the  meridian  of  the  places  passeB  under 
the  sun.     In  the  lapse  of  24  hours,  the  rotation  of  the 
earth  on  its  axis  brings  all  its  meridians  under  the  sun  in 
succassion,  or,  which  is  the  same  thing,  the  sun  appears  to 
pass  in  succession  all  the  meridians  of  the  earth.     Henoe, 
noon  continually  travels  westward  at  the  rate  of  15*  in  an 
hour,  making  the  circuit  of  the  earth  in  24  houw.     The 
difference  between  the  time  of  day,  or  local  time  as  it  is 
called,  at  any  two  places,  will  be  in  proportion  to  the  diflbr- 
ence  of  longitude,  amounting  to  one  hour  for  eveiy  16 
degrees  of  longitude,  four  minutes  for  every  degree,  and 
so  on.      Vice  versa,  if  at  the  same  real  moment  of  time 
we  can  determine  the  local  times  at  two  different  places, 
the  difference  of  these  times,  multiplied  by  15,  will  give 
the  difference  of  longitude. 


in  degrees, 

hours,  like 

minutes  and 

ascension  of 

ich  it  passes 

'nres,  can  be 
or  a  second 

iponding  de- 
the  degree. 

>y  the  initial 

=4"> 
'=4» 

ring  our  civil 
en  that  it  is 
hen  the  sun 
k  with  more 
PMses  under 
ttion  of  the 
f  the  sun  in 
n  appears  to 
'h.     Hence, 


GHANOB  OF  DA  Y. 


33 


I)fl6« 


in  an 


lours.  The 
t'm0  as  it  is 
» the  diflbr. 
w  eveiy  15 
Iflgrae,  and 
nt  of  time 
«nt  phu»s, 
',  will  give 


Tlie  longitudes  of  places  are  determined  astronomically 
on  this  principle.  Astronomers  are,  however,  in  the 
habit  of  expressing  the  longitude  of  places  on  the  earth 
like  the  right  ascensions  of  the  heavenly  bodies,  not  in 
degrees,  but  in  hours.  For  instance,  instead  of  saying 
that  Washington  is  77"  3'  west  of  Greenwich,  we  com- 
monly say  that  it  is  5  hours  8  minutes  12  seconds  west, 
meaning  that  when  it  is  noon  at  Washington  it  is  5  hours 
8  minutes  12  seconds  after  noon  at  Greenwich.  This 
course  is  adopted  to  prevent  the  trouble  and  confusion 
which  might  arise  from  constantly  having  to  change  hours 
into  degrees,  and  the  reverse. 

A  question  frequently  asked  in  this  connection  is. 
Where  does  the  day  change  ?  It  is,  we  will  suppose,  Sun- 
day noon  at  Washington.  That  noon  travels  all  the  way 
round  the  earth,  and  when  it  gets  back  to  Washington 
again  it  is  Monday.  Where  or  when  did  it  change  from 
Sunday  to  Monday  ?  We  answer,  wherever  people  choose 
to  make  the  change,  l^avigators  make  the  change 
occur  in  longitude  180°  from  Greenwich.  As  this  meri- 
dian lies  in  the  Pacific  Ocean,  and  scarcely  meets  any  land 
through  its  course,  it  is  very  convenient  for  this  purpose. 
If  its  use  were  universal,  the  day  in  question  would  be 
Sunday  to  all  the  inhabitants  east  of  this  line,  and  Mon- 
day to  every  one  west  of  it.  But  in  practice  there  have 
been  some  deviations.  As  a  general  rule,  on  those  islands 
of  the  Pacific  which  are  settled  by  men  travelling  east, 
the  day  would  at  first  be  called  Monday,  even  tiiough 
they  might  cross  the  meridian  of  180**.  Indeed  the  Rus- 
sian settlers  carried  their  count  into  Alaska,  so  that  when 
our  people  took  possession  of  that  territory  they  found 
that  the  inhabitants  called  the  day  Monday,  when  they 
themselves  called  it  Sunday.  These  deviations  have,  how- 
ever, almost  entirely  disappeared,  and  with  few  exceptions 
the  day  is  changed  by  common  consent  in  longitude  ) '  '° 
from  Greenwich. 


84 


A8TR0N0MT. 


g  e.  DETEBMnrATIOirS  of  TEBSB8TBIAL  LONOI- 

TUDES. 

We  have  remarked  that,  owing  to  the  rotation  of  the  earth, 
there  is  no  such  fixed  correspondence  between  meridians  on 
the  earth  and  aniong  the  stars  as  there  is  between  latitude  on 
the  earth  and  declination  in  the  heavens.  The  observer 
can  always  determine  his  latitude  by  finding  the  declination 
of  his  zenith,  but  he  cannot  find  his  longitude  from  the 
right  ascension  of  his  zenith  with  the  same  facility,  be- 
cause that  right  ascension  is  constantly  changing.  To  deter- 
mine the  longitude  of  a  place,  the  element  of  time  as  mea- 
sured by  the  diurnal  motion  of  the  earth  necessarily  comes 
in.  Let  us  once  more  consider  the  plane  of  the  meridian 
of  a  place  extended  out  to  the  celestial  sphere  so  as  to 
mark  out  on  the  latter  the  celestial  meridian  of  the  place. 
Consider  two  such  places,  Washington  and  San  Francisco 
for  example ;  then  there  will  be  two  such  celestial  meri- 
dians cutting  the  celestial  sphere  so  as  to  make  an  angle  of 
about  forty-five  degrees  with  each  other  in  this  case.  Let 
the  observer  imagine  himself  at  San  Francisco.  Then  he 
may  conceive  the  meridian  of  Washington  to  be  visible 
on  the  celestial  sphere,  and  to  extend  from  the  pole  over 
toward  his  south-east  horizon  so  as  to  pass  at  a  distance  of 
about  forty-five  degrees  east  of  his  own  meridian.  It 
wonld  appear  to  him  to  be  at  rest,  although  really  both 
his  own  meridian  and  that  of  Washington  are  moving  in 
consequence  of  the  earth's  rotation.  Apparently  the  rtan 
in  their  course  will  first  pass  the  meridian  of  Washington, 
and  about  three  hours  later  will  pass  his  own  meridian. 
Now  it  is  evident  that  if  he  can  determine  the  interval 
which  the  star  requires  to  pass  from  the  meridiftn  of  Wash- 
ington to  that  of  his  own  place,  he  will  at  once  have  the 
difference  of  longitude  of  the  two  places  by  simply  turn- 
ing the  interval  in  time  into  degrees  at  the  rate  of  fifteen 
degrees  to  each  hour. 

Essentially  the  same  idea  may  perhaps  be  more  raa^ftiy 
grasped  by  considering  the  star  as  apparently  piassing  over 


LONOITUDE. 


85 


ion  of  the  earth, 
in  meridians  on 
'een  latitude  on 
The  observer 
the  declination 
|tude  from  the 
e  facility,  be- 
ing.   To  deter- 
>f  time  as  mea- 
cessarily  comes 
f  the  meridian 
>here  so  as  to 
I  of  the  pkce. 
San  Francisco 
celestial  men- 
kke  an  angle  of 
[this  case.    Let 
^.     Then  he 
n  to  be  visible 
I  the  pole  over 
It  a  distance  of 
meridian.      It 
arh  really  both 
are  moving  in 
rentlj  the  stars 
f  Washington, 
own  meridian. 
«  the  interval 
(Han  of  Wash- 
once  have  the 
Y  simply  tum- 
nte  of  fifteen 

more  rea(|lly 
f  passmg  over 


gg-feiiiwa^saaajg 


the  snccessive  terrestrial  meridians  on  the  surface  of  the 
earth,  the  earth  being  now  supposed  for  a  moment  to  be 
at  rest.  If  we  imagine  a  straight  line  drawn  from  the 
centre  of  the  earth  to  a  star,  this  line  will  in  the  course  of 
twenty-four  sidereal  hours  apparently  make  a  complete 
revolution,  passing  in  succession  the  meridians  of  all  the 
places  |)n  the  earth  at  the  rate  of  fifteen  degrees  in  an  hour 
of  sidereal  time.  If,  then,  Washington  and  San  Francisco 
are  forty-five  degrees  apart,  any  one  star,  no  matter  what 
its  declination,  will  require  three  sidereal  hours  to  pass 
from  the  meridian  of  Washington  to  that  of  San  Francisco, 
and  the  sun  will  require  tluee  gdar  iiours  for  the  same 
passage. 

Whichever  idea  we  adopt,  the  result  will  be  the  same  : 
difference  of  longitude  is  measured  by  the  time  required 
for  a  star  to  apparently  pass  from  the  meridian  of  one 
place  to  that  of  another.  There  is  yet  another  way  of 
defining  what  is  in  effect  the  same  thing.  The  sidereal 
time  of  any  place  at  any  instant  being  the  same  with  the 
right  ascension  of  its  meridian  at  that  instant,  it  follows 
that  at  any  instant  the  sidereal  times  of  the  two  places  will 
differ  by  the  amount  of  the  difference  of  longitude.  For 
instance :  suppose  that  a  star  in  0  hours  right  ascension  is 
crossing  the  meridian  of  Washington.  Then  it  is  0  hours 
of  local  sidereal  time  at  Washington.  Three  hours  later 
the  star  will  have  reached  the  meridian  of  San  Francisco. 
Then  it  will  be  C  hours  local  sidereal  time  at  San  Fran- 
cisco. Hence  the  difference  of  longitude  of  two  places  is 
measured  by  the  difference  of  their  sidereal  times  at  the 
same  ins^  At  of  absolute  time.  Instead  of  sidereal  times, 
we  may  equally  well  take  mean  times  as  measured  by  the 
sun.  It  being  noon  when  the  snn  crosses  tiie  meridian  of 
any  place,  and  the  snn  requiring  three  hours  to  pass  from 
the  meridian  of  Washington  to  that  of  San  Francisco,  it 
follows  that  when  it  is  noon  at  San  Francisco  it  is  three 
o'olodc  in  the  afternoon  at  Washington.* 

*  The  dUtawnoe  <rf  kogitiide  thus  depends  opon  the  anffular  dU- 
Uuu$^1tmtlrMmeHdiaiu,  and  not  upon  the  motioa  of  a  celestial  body. 


fiiSC 


j£.m- 


SSSE" 


36 


ABTRONOMT. 


The  whole  problem  of  the  determination  of  terrestrial 
longitudes  is  thns  reduced  to  one  of  these  two  :  either 
to  find  the  moment  of  Greenwich  or  Washington  time 
corresponding  to  some  moment  of  time  at  the  place 
which  is  tc  bo  determined,  or  to  find  the  time  required 
for  the  sun  or  a  star  to  move  from  the  meridian  of  Green- 
wich or  Washington  to  that  of  the  place.  If  it  were 
possible  to  fire  a  gun  every  day  at  Washington^  noon 
which  could  be  heard  in  an  instant  all  over  the  earth, 
then  observers  everywhere,  with  instruments  to  deter- 
mine their  local  time  by  the  sun  or  by  thr:  stars,  would  be 
able  at  once  to  fix  their  longitudes  by  noting  the  hour, 
minute,  and  second  of  local  time  at  which  the  gun  was 
heard.  As  a  matter  of  fact,  the  time  of  Washington  noon 
is  daily  sent  by  telegraph  to  many  telegraph  stations,  and 
an  observer  at  any  such  station  who  knows  his  local  time 
can  get  a  very  close  value  of  his  longitude  by  observing  the 
local  time  of  the  arrival  of  this  signal.  Human  ingenuity 
has  for  several  centuries  been  exercised  in  the  effort  to  in- 
vent some  practical  way  of  accomplishing  the  equivalent 
of  such  a  signal  which  could  be  used  anywhere  on  the 
earth.  The  British  Government  long  had  a  standing  offer 
of  a  reward  of  ten  thousand  pounds  to  any  person  who 
would  discover  a  practical  method  of  determining  the  lon- 
gitude at  sea  with  the  necessary  accuracy.  This  reward 
was  at  length  divided  between  a  mathematician  who  con- 
structed improved  tables  of  the  moon's  motion  and  a 
mechanician  who  invented  an  improved  chronometer. 
Before  the  invention  of  the  telegraph  the  motion  of  the 
moon  and  the  transportation  of  ohronometen  afforded 
almost  the  only  practicable  and  widely  extended  methods 
of  solving  the  problem  in  question.  The  invention  of 
the  telegraph  offered  a  third,  far  more  perfect  in  its  appli- 

and  hence  the  longitude  of  a  place  is  the  same  whether  ezprened  as  a 
difference  of  two  siderral  times  or  of  two  solar  times.  Tab  longitude 
of  Washington  west  from  Greenwich  is  5^  8"  or  77",  and  this  Is.  in  UicX, 
the  ratio  of  the  anguUr  distance  of  tlie  meridian  of  Washington  frmn 
that  of  Greenwich  to  860°  or  24^.  It  is  thus  phiin  that  the  Iragitude  is 
the  difference  of  the  simultaneous  local  times,  whether  solar  or  sidereaL 


kib 


'wi&jjaMywMiMfefa#»rfi,^^^^ 


LONGITUDE  BY  CHRONOMETERS. 


37 


)f  terrestrial 
Itwo;  either 
fington  time 
ft  tlie  place 
|me  required 
m  of  Green. 

If  it  were 
fngtoni'  noon 

the  earth, 
tfl  to  deter- 
rs,  would  be 
g  the  hour, 
'he  gun  was 
ington  noon 
itations,  and 
B  local  time 
bserving  the 
tn  ingenuity 
effort  to  in- 

>  equivalent 
Here  on  the 
anding  offer 
person  who 
ing  the  Ion- 
Phis  reward 
ui  who  con< 
tion  and  a 
uonometer. 
tion  of  the 
n  afforded 
id  methods 
vention  of 
n  its  appli. 

nNwnedu  • 
lie  longitude 
>tais.infM3t. 
ilagton  frmn 

>  longitude  is 
rorddereaL 


cation,  but  necessarily  limited  to  places  in  telegraphic 
communication  with  each  other. 

Longitude  by  Motion  of  the  Moon. — When  we  de- 
scribe the  motion  of  the  moon,  we  shall  see  that  it  moves 
eastward  among  the  stars  at  the  rate  of  a)K)ut  thirteen  de- 
grees per  day,  more  or  less.  In  other  words,  its  right  as- 
cension is  constantly  increasing  at  the  rate  of  a  degree  in 
something  less  than  two  hours.  If,  then,  its  right  ascension 
can  bo  predicted  in  advance  for  each  hour  of  Greenwich 
or  Washington  time,  an  observer  at  any  point  of  the 
earth,  by  noting  the  local  time  at  his  station,  when  the 
moon  has  any  given  right  ascension,  can  thence  determine 
the  corresponding  moment  of  Greenwich  time  ;  and  hence, 
from  the  difference  of  the  local  times,  the  longitude  of  his 
place.  The  moon  vrill  thus  serve  the  purpose  of  a  sort  of 
clock  running  on  Greenwich  time,  upon  the  face  of  which 
any  observer  Mrith  the  proper  appliances  can  read  the 
Greenwich  hour.  This  method  of  determining  longitudes 
has  its  difficulties  and  drawbacks.  The  motion  of  the 
moon  is  so  slow  that  a  very  small  change  in  its  right  ascen- 
sion will  produce  a  comparatively  large  one  in  the  Green- 
wich time  deduced  from  it — about  27  times  as  great  an 
error  in  the  deduced  longitudes  as  exists  in  the  determi- 
nation of  the  moon's  right  ascension.  With  such  instru- 
ments as  an  observer  can  easily  carry  from  place  to  place, 
it  is  hardly  possible  to  determine  the  moon's  right  ascen- 
sion within  five  aeoonds  of  are ;  and  an  error  of  this 
amount  will  produce  an  error  of  nine  seconds  in  the 
Greenwich  time,  and  henoe  of  two  miles  or  more  in  his 
deduced  longitude.  Besides,  the  mathematical  processes 
of  dedndng  from  an  observed  right-ascension  of  the  moon 
the  corresponding  Greenwich  time  are,  under  ordinary 
oircumstances,  too  troublesome  and  laborious  to  make  this 
method  of  value  to  the  navigator. 

Tmnaportfttioii  of  Ghxonometers. — ^The  transportation 
of  ohronometera  affords  a  simple  and  convenient  method 
of  obtaining  the  time  of  the  standard  meridian  at  any 
moment.     The  observer  sets  his  chronometer  as  nearly  as 


38 


ASTnONOMT. 


possible  on  Greenwich  or  Washington  time,  and  deter- 
mines its  correction  and  rate.  This  he  can  do  at  any  sta- 
tion of  which  the  longitude  is  correctly  known,  and  at 
which  the  local  time  can  be  determined.  Then,  wherever 
he  travels,  he  can  read  the  time  of  his  standard  meridian 
from  the  face  of  his  chronometer  at  any  moment,  and 
compare  it  with  the  local  time  determined  with  his  transit 
instrument  or  sextant.  The  principal  error  to  which  this 
method  is  subject  arises  from  the  necessary  uncertainty  in 
the  rate  of  even  the  best  chronometers.  This  is  the 
method  almost  universally  used  at  sea  where  the  object  is 
simply  to  get  an  approximate  knowledge  of  the  ship's 
position. 

The  accuracy  can,  however,  be  increased  by  carrying  a 
large  number  of  chronometers,  or  by  repeating  the  de- 
termination a  number  of  times,  and  this  method  is  often 
employed  for  fixing  the  longitudes  of  seaports,  etc. 
Between  the  years  1848  and  1855,  great  numbers  of  chro- 
nometers were  transported  on  the  Cunard  steamers  plying 
between  Boston  and  Liverpool,  to  determine  the  difference 
of  longitude  between  Greenwich  and  the  Cambridge  Ob- 
servatory, Massachusetts.  At  Liverpool  the  chronometers 
were  carefnily  compared  with  Greenwich  time  at  a  >ocal 
observatory — ^that  is,  the  astronomer  at  Liverpool  found 
the  error  of  the  chronometer  on  its  arrival  in  the  ship, 
and  then  again  when  the  ship  was  about  to  sail.  When 
the  chronometer  reached  Boston,  in  like  manner  its  error 
on  Cambridge  time  was  determined,  and  the  det«inination 
was  repeated  when  the  ship  was  about  to  return.  Having 
a  number  of  such  determinations  made  alternately  on  the 
two  sides  of  the  Atlantic,  the  rates  of  the  cfaronometers 
could  be  determined  for  each  double  voyage,  and  thus  the 
error  on  Greenwich  time  could  be  calculated  for  the  mo- 
ment of  each  Cambridge  comparison,  and  the  moment  of 
Cambridge  time  for  each  Greenwich  xiomparison. 

Longitade  by  the  Bectrio  Tdegzmph. — ^As  soon  as  the 
electric  telegraph  was  introdaced  it  was  seen  by  American 


"OMns 


mmm^fimi^^lmk^M'^-^^^'' 


|e,  and  deter- 
lo  at  any  sta- 
liown,  and  at 
pen,  wherever 
lard  meridian 
inonient,  and 
|ith  Lis  transit 
to  which  this 
incertaintj  in 
This  is  the 
the  object  is 
>f  the  ship's 

by  carrying  a 
ftting  the  de- 
ithod  is  often 
seaports,   etc. 
ibers  of  chro- 
iamers  plying 
the  difference 
unbridge  Ob- 
chronometers 
ime  at  a  .'ocal 
erpool  found 
in  the  ship, 
saiL     When 
mer  its  error 
letennination 
rn.    Having 
utely  on  the 
shronometers 
and  thus  the 
for  the  mo- 
>  moment  of 
ion. 

i  soon  as  the 
y  American 


LOyOITUDE  BT  TBLEORAPn.  •• 

astronomers  that  wo  here  had  a  method  of  determining 
longitudes  wliicli    for    rapidity  and  convenience   would 
supersede  all  others.     The  first  application  of  this  method 
was  mode  in  1844  between  Washington  and  Baltimore, 
under  the  direction  of  the  late  Admiral  Charles  Wilkes, 
U.  8.  N.  During  the  next  two  years  the  method  was  intro- 
duced into  the  Coast  Survey,  and  the  difference  of  longitude 
between  New  York,  Philadelphia,  and  Washington  was 
thus  determined,  and  since  that  time  this  method  has  had 
wide  extension  not  only  in  the  United  States,  but  between 
America  and  Europe,  in  Europe  itself,  in  the  East  and  West 
Indies,  and  South  America.     The  principle  of  the  method 
is  extremely  simple.  Each  place,  of  which  the  difference  of 
time  (or  longitude)  is  to  be  determined,  is  furnished  with  a 
transit  instrument,  a  clock  and  a  chronograph  ;  instruments 
described  in  the  next  chapter.     Each  clock  is  placed  in 
galvanic  communication  not  only  with  its  own  chronograph, 
but  if  necessary  is  so  connected  with  the  telegraph  wires 
that  it  can  record  its  own  beat  upon  a  chronograph  at  the 
other  station.     The  observer,  looking  into  the  telescope 
and  noting  the  crossing  of  the  stars  over  the  meridian, 
can,  by  his  signals,  record  the  instant  of  transit  both  on  his 
own  chronograph  and  on  that  of  the  other  station.     The 
plan  of  making  a  determination  between  Philadelphia  and 
Washington,   for  instance,  was  essentially  this :   When 
some  previously  selected  star  reached  the  meridian  at  Phil- 
adelphia, the  observer  pointed  his  transit  upon  it,  and  as 
it  crossed  the  wires,  recorded  the  signal  of  time  not  only 
on  his  own  ohron<^praph,  but   on  that  at  Washington. 
About   eight    minutes   afterward  the    star  reached  the 
meridian  at  Washington,  and  there  the  observer  recorded 
its  transit  both  on  his  own  chronograph  and  oa  that  at 
Philadelphia.     The  interval  between  the  transit  over  the 
two  places,  as  measured  by  either  sidereal  clock,  at  once 
gave  the  difference-  of  longitude.     If  the  record  was  in- 
stantaneous at  the  two  stations,  this  interval  ought  to  be 
the  same,  whether  read  off  the  Phihtdelphia  or  the  Wash- 


'to  ARTHOiTOMY. 

ington  chronogrupli.  It  was  found,  however,  tliat  there 
wan  a  difleronce  of  a  Binall  fraction  of  a  second,  ariHing 
from  the  fact  tliat  electricity  re(£uired  an  interval  of  time, 
minute  but  yet  appreciable,  to  puss  between  the  two 
cities.  The  PhiUdelphia  record  was  a  little  too  late  in 
being  recorded  at  Washinj^ton,  and  the  Washington  one  a 
little  too  late  in  being  recorded  at  Philadelphia.  We 
may  illustrate  this  by  an  example  as  follows  : 

Suppose  £  to  Ih3  a  station  one  degree  of  longitude  eaat 
of  another  station,  W  ;  and  that  at  each  station  there  is  a 
clock  exactly  regulated  to  the  time  of  its  own  place,  in 
which  case  the  clock  at  E  will  l)e  of  course  four  minutes 
fast  of  the  clock  at  W  ;  let  us  also  suppose  that  a  signal 
takes  ft  quarter  of  a  second  to  pass  from  one  station  to  the 
other  : 

Then  if  the  obgerver  at  E  sends  a  nignal  to  W  at  exactly 

noon  by  his  clock 12''   O"  COO 

It  will  be  received  at  W  at * n*"  66">  0'.25 

Showing  an  apparent  difference  of  time  of S"  fiiCTS 

Then  if  the  observer  at  W  sends  a  signal  at  noon  by  his 

dock la*  0"  COO 

It  will  be  received  at  E  at  12''  4""  0".a6 

Showing  an  apparent  difference  of  time  of 4"  0*.25 

One  half  the  sum  of  these  differences  is  four  minutes» 
which  is  exactly  the  difference  of  time,  or  one  degree  of 
longitude ;  and  one  half  their  difference  is  twenty-live 
hundredths  of  a  second,  the  time  taken  by  the  electric  im- 
pulse to  traverse  the  wire  and  telegraph  instruments. 

This  is  technically  called  the  "wave  and  armature 
time." 

We  have  seen  that  if  a  signal  could  be  made  at  Wash- 
ington noon,  and  observed  by  an  observer  anywhere  sit- 
uated who  knew  the  local  time  of  hia  station,  his  longi- 
tude would  thus  become  known.  This  principle  is  often 
employed  in  methods  of  determining  longitude  other  than 
those  named.     For  example,  the  instant  of  the  banning 


that  there 
Olid,  ariHiiig 
•vul  of  time, 
ton  tlio  two 
too  lato  in 
ington  ono  a 
slphia.     We 

ngitudo  eaat 
>ii  there  ig  a 
vn  place,  in 
oar  minutes 
lat  a  signal 
tttion  to  tlie 


la*  o-o-.oo 

.ll*>86">0'.a5 


ig 


S"  59'.76 

la'o-'O'.oo 
la"-  4-  c.aa 

i-O-.M 


ur  minutegf 

le  degree  of 

twenty-liye 

electric  iin- 

ments. 

d  armature 

le  at  Wash- 
ywhere  dt- 
,  his  long!- 
pie  is  often 
I  other  than 
9  beginning 


TUKOttY  OF  THM  bVUKHK. 


41 


.„.  .nOuM,  of  an  «=Up»  of  ....  -J"  *^*:^ --"^^J 
.v.rfm.tlv  dotln  to  p  lenoineiion.  it  this  w  ooiwrvwu  j 
wo  obirve™,  and  these  in.t«iU  noted  by  each  in  the 
Wal  ttieo?  his  station,  then  the  difference  of  thej« 
W  S  (subject  to  small  correction,  due  U,  pa«Uax, 
etc.)  will  bo  the  difference  of  longitude  of  the  two  aw 

^'^Tho  satellites  of  Jupiter  suffer  ecUpaes  frequently,  and 
the  cCuw^rand  wihington  times  of  theje  phenomena 
a^  ooZZa  and  set  down  in  the  Nautical  Almanac    Ob- 

L'vatSon-  of  these  at  any  -^*!<>V'L*tf  S'rl^^^^^^^^ 
ence  of  longitude  between  tlus  rtation  and  ^^'''^'''V'J 
wlington^  As,  however,  they  require  a  larger  tele- 
ZeTnd  a  higher  magnifying  power  than  can  Ik,  used  at 
t^rtWB  meth^  is  not  a  practical  one  for  navigators. 

8  7.  ItATHBIATIOAL  Iggg  OP  THB  0«L«TIAL 

In  thU  •xplanatKm  «' »'«  » tX%*ir7nt*i^^^^^^^^^^ 
the  heavenly  bodies  to  «*«>«•  «°*of  the  rSlor  is  necesgarlly  pre- 
Ipherlcal  trUnometry  on  the  ~^^  „,        f^^on 

gUpposed.  >•  8«i«'!l'5?i*lolJtrrclroWs  u  follow. : 

thi  sphere  i«refen*dto  axed  pgntoor^^^^^    U  Uken  as  a  bwis, 

A  M»"«nt»ie:!r*  S^S"u..  b<SVl?t«  angular  dUUnce  from 
„d  the  first  S;«^'"J*»T«i,rI,  S  is  taken^  the  fundwnenUl 
this  circle.  When  the  •^•^'^^"rf^  called  Latitude  ;  on  the 
circle,  this  dlrta«je  J^^JJjJjjJJJ^J^i  Declination.    If 

't'^^^^^^I^^S^ScircXe  thedUUnceiajMll^ 
thehodaonls  tAen  MiMran«™  »bovethe  horison. 

AUituds.  Altltoda  to  «»J^*^oBDOsite  sides  of  the  circle,  dis- 
todiBti^^VHA^^^^^J'^^Mj  positive  quantltie^ 
tance.onoMsldeawrv2J  "  "^"^  ^  ^  the  equator  the 
«Bd  on  the  otiwr  •«•  "  "^iSiion  the  upper  side,  are  considered 
north  •«•,  and »«  *f  •J.J'JgJ'SIhe  hoK  Ito  altitude  U  ne«- 
8S»'2d  S^ZSHi^i^^^  of  U.e  earthB  equator  Is.  in 
•S^^  lKSd£5f^"d2&  another  elided  «nl«i 
or'^dJL^ffSS^-reSiU    The  lund«n.nUl  circle  I. 


dfAiM  lU jojinon .    ri  ^^    poMUon  on  •  -k!"-?  - 


lines,  wWch 

•   ■  are  lu 

ccHyrdl* 


48 


ASTRONOMY. 


cTery where  W  from  its  positiTe  pole,  P.    Hence,  if  A  is  tlie  position 

of  a  star  or  other  point  on  tlie 
sphere,  and  we  put 

tf,   its   declination    or  altitude. 
=  aA. 

p,  its  polar  or  senith  distance 
=PA,  we  shall  have 


or. 


p  =  90"— d. 


Fio.  la. 


If  the  star  is  south  of  the 
fundamental  circle,  at  B  for  ex- 
ample, d  being  negative  p  will  ex- 
ceed 00°.  This  quantity  p  may 
range  from  zero  at  the  one  pole 
to  180°  at  the  other,  and  will  al- 

T»  i.  ««  ♦».:«  *  ^    u         .     V'^^  ^  algebraically  positive. 

It  is  on  this  account  to  be  preferred  to  S,  though  less  frequently 

II.  The  second  co-ordinate  required  to  fix  a  position  on  the  celes- 
tial or  terrestrial  sphere  is  longitude,  riffht  ateetuion,  or  azimuth,  ac- 
cording to  tiie  fundamental  plane  adopted.     It  is  expressed  by  the 
position  of  the  great  circle  or  meridian  P  A  a  P  which  passes 
wirough  the  position  from  one  pole  to  the  other,  at  right  angles  to 
the  fundamental  circle.  An  arbitrary  point,  F  for  instance,  is  chosen 
on  this  latter  circle,  and  the  longitude  is  the  angle  Va'inm  this 
point  to  the  intersection  of  the  meridUn  or  vertical  circle  passing 
through  the  object.    We  may  also  consider  it  as  the  angle  V/*  3 
which  the  circle  passing  through  the  object  makes  with  the  circle 
P  V,  because  this  angle  is  equal 
to  Va.    The  angle  is  commonly 
counted  from  V  toward  the  right, 
and  from  0°  round  to  860',  so  as 
to  avoid  using  negative  angles. 
If  the  observer  is  stationed  in 
the  centre  of  the  sphere,  with  his 
head  toward  the  positive  pole  P, 
the  positive  direction  should  be 
from  right  to  left    around    the 
sphere.     When    the  horiion  is 
taken  as  the  fundamental  circle 
or  plane,  this  secondary  co-ordi- 
nate is  called  the  arimiah,  and 
should  be  counted  from  the  soutii 
point  toward  east,  or  from  the 
north  point  toward  west,  but  is 
commonly  counted  the  other  way.    It  may  be  defined  as  the  ancnlar 
distance  of  the  vertical  circle  passing  through  the  object  from  the 
south  point  of  the  horiion. 


litti 


A  is  the  position 
er  point  on  the 
put 

on   or  altitude, 


zenith  distance 
have 

=  90°, 
r-6. 

s  south  of  the 
cle,  at  B  for  ex- 
Bgativep  will  ex- 
quantity  p  may 
at  the  one  pole 
her,  and  will  al- 
aically  positive, 
less  frequently 

n  on  the  celes- 
or  azimuth,  ac- 
pressed  by  the 
which  passes 
right  angles  to 
tance,  is  chosen 
Va,  from  this 
I  circle  passing 
le  angle  VPA 
with  the  circle 


THEORY  OF  THE  BPHERS. 


48 


The  fto«ran!/fe  of  a  sUr  is  measured  by  the  interral  which  has 

r,  the  sidereal  time,  v.n  k.-« 

a,  the  right  ascension  of  the  object,  we  shall  have 

Hour  angle,  A  =  t  —  «. 

Tt  will  be  neeatiTe  before  the  object  has  passed  the  meridian,  and 
\-  n-^S^?  It  differs  from  right  ascension  only  m  the  point 
r'''-hVcni^eckonSandThe '^direction  which 'is  conrifoed 
Sive  The  ghTa^eSon  is  measured  toward  the  east  from  a 
Suthe  yernal  equinox)  which  is  fixed  among  the  stars^.while  the 
C  angle  S  mewured  toward  the  west  from  the  mendmnof  the 
Er^er,  which  meridian  is  consUntly  in  motion,  owing  to  the 

•*m'h^t"xt  to  show  the  trigonome^icri  relations  which  subsist 
between  Se  hour  angle,  decUnation,  altitude,  and  aaimuth.    Let 


as  the  angular 
>bject  from  ttie 


Fm.l4 


Pig.  14  be  a  view  of  the  celestial  hemiaphere  which  is  above  tiie 
hraixon,  as  seen  from  the  eaat    Wetiienhave: 

HER  F,  the horiaon. 

P,  the  pole. 

Z,  the  lenith  of  the  observer. 

ir  Jf  Z  P  JJ;  the  meridian  of  the  observer. 

P  Ji;  the  latitude  of  the  observer,  which  call  f. 

?C'S.1Litf  S£»«»*.-' = •«•  -  ■^'"«»"- 

Ta,i\M  altitude,  which  call  a, 
za,i\»  aenitii  diataooa  =  W"  -  «• 
MZS,  itoaaimuth,  =  180'  -anrie  8  Z  P. 
Z  P  ^  its  hour  an^e,  which  call  *. 

The  spherical  triangle  Z  P  -8,  of  which  the  angles  are  formed  by 


u 


ASTRONOMY. 


the  xenith,  the  pole,  and  the  star,  is  the  fundamental  triangle  of  our 
problem.  The  latter,  as  commonly  solved,  may  be  put  into  two  forms. 

I.  Givi-n  the  latitude  of  the  place,  the  declination  or  polar  dis- 
tance of  the  star,  and  its  hour  angle,  to  find  its  altitude  and  azimuth. 

We  have,  by  spherical  trigonometry,  considering  the  angles  and 
sides  of  the  triangle  Z  P  8  : 

con  Z  S  =  coB  PZcoB  PS  +  sin  P  Z  sin  PS  cos  P. 
Bin  ZS  coa  Z  =  sia  PZ  eoa  PS  — coA  PZ  sin  PS  cos  P. 
sin  ZSain  Z  =  Bin  PS  sin  P. 

By  the  above  definitions, 

Z  S=90°  —  a,  (a  being  the  altitude  of  the  star). 

PZ=90°  —  ^,  (^  being  the  latitude  of  the  place). 

PS  =  90'  —  d,  (6  being  the  declination  of  the  star,  +  when  north). 

P  =  h,  the  hour  angla 

Z  =  180°  —  t,  (2  being  the  azimuth). 

Making  these  substitutions,  the  equation  becomes : 

sin  a  =  sin  f  sin  4  +  coa  f  cos  4  cos  A. 
COR  a  cos  •  =  —  COB  ik  sin  ^  +  sin  f  coa  '  cos  A. 
cos  a  sin  •  =      cos  J  sin  A. 

From  these  equations  sin  a  and  cos  a  may  be  obtained  separately, 
and,  if  the  computation  is  correct,  they  wul  give  thi>  i..  <3  val'je  of  a. 
If  the  altitude  only  is  wanted,  it  mayv.1be  obiaim  1  f  >  t*>e  first 
equation  alone,  which  may  be  transformed  in  Tarioua  .  xy^  ained 

in  works  on  trigonometry. 

II.  Given  the  latitude  of  the  place,  the  deelination  of  a  star,  and 
its  altitude  above  the  hwison,  to  find  its  hour  ande  and  (if  its  right 
ascension  is  known)  the  sidereal  timi  when  it  liaa  the  given  altitude. 

We  find  from  the  first  of  the  above  equations. 


cosA  = 


sin  a  — 'lin  ^  sin  dl. 


or  we  may  use : 


sin'iA  =  i 


cos  ^  008  i 


COS  (f  —  «t)  —  sin  o 


cos  ^  000  4 

Having  thus  found  A,  we  have 

Sidereal  time  s=  A  +  cr, 

a  being  the  star's  right  ascension,  and  the  hour  angle  A  being  changed 
into  time  by  dividing  by  16. 

ni.  An  interesting  form  of  this  last  problem  arises  when  we  sup- 
pose a  sa  0,  which  is  the  same  thii^;  as  supposing  the  star  to  be  in 


tal  triangle  of  our 
tit  into  two  forms. 

ion  or  polar  dis- 
,ude  and  aumuth. 
ig  the  angles  and 


1  P  S  cos  P. 
\PScmP. 


ir,  +  when  north). 


6  cos  h. 


tabled  separately, 
It,  b.  .aval'jeof  a. 
1 1  r  >  ♦»•«  arst 
»  .    <       xit^'vined 


Ion  of  a  star,  and 
e  and  (if  its  right 
the  given  altitude. 


le  A  being  ebanged 


iseswhenwe  au 


ABlRONOMr. 


46 


the  horizon,  and  therefore  Xo  be  rising  or  setting     ^s  •  t'blj 

time  between  its  "«"«.  *""':*  P^Ji^s  interval  is  caUed  the  $emir 
tween  this  passage  and  its  setting.    This  mtervai  «  c~. 

diurnal  are,  and  by  doubling  it  ^^^— ^ 

we  have  the  time  between  the 
rising  and  setting  of  the  star  or 
other  object  Putting  a  =  0  in 
the  preceding  expression  for  cos 
h  we  find  for  the  semi  diurnal 
arc  A, 

_       wn  ^  sin  j 
CCS  ft  —  —  -^  ^  cos  S 

=  —  tan  ^  tan  d, 

and  the  arc  during  which  the 
sUr  is  above  the  horiion  is  2  *. 

Prom  this  formula   may  be  

deduced  at  once  many  of  the  ^bbbi^^^^^^^^ 

results  given  in  the  preceding  j.^  IB.— cpm  um  umtM  mro- 

S6Ction8.  HAIi  ABC& 

(I).  At  the  poles  f  =  ,^'  ^^  r  _  »„ftnitv     But  the  cosine  of 
tan  *  =  infinity,  and  thw^JJw  cm  A  ^^  ^«        ^^  ^„^ 

an  angle  can  never  be  g'«'*«' .IS"  "^^L' e^  .  gjr  »rthe  pole  can 
of  A  which  fulfite  the  condition.    Hence,  a  siar  at  w»  i~ 

neither  rise  nor  set  .  _  ao  ♦.n  a  =  0  whence  cos  A  =  0, 

.  <'>in^*  *;«T^  iXihaterer  beT  *TO.  brinj  a  semicircum. 
{e^nSrAVhia7en\?'boj£*rh.lf  the  time  above  the  hori«.n  to 

^e  t^aL-SiSu^tTeJielirve^h^^^^ 

tude  of  the  observer.    Here  we  except  *«  I^|«;  ^'^^.S  *.  ^tuok 


Und 


tand 


Ig  the  star 


ire  aup- 
to  be  in 


«••*  =  "  SSI  "■       tan  (90°  -  f) 
wbMi<tapo«ltiT«,oos»tan«8»tlTe,andA>W,»»?'  *"« 


46 


A8TR0N0MT. 


negative  i,  cos  h  is  positive,  A  <  90%  2  A  <  180°.  Hence,  in  north- 
em  latitudes,  a  northern  sUr  is  more  than  half  of  the  time  above  the 
horizon,  and  a  soi'them  star  loss.  In  the  southern  hemisphere,  f  and 
tan  f  are  negative,  and  the  case  is  reversed.  ^ 

(6).  If,  in  the  preceding  case,  the  declination  of  a  body  is  supposed 
constant  and  north,  then  the  greater  we  make  ♦  the  greater  the  nega- 
tive value  of  cos  h  and  the  greater  h  itself  will  be.  Considering,  m 
succession,  the  cases  of  north  and  south  declination  and  north  and 
south  latitude,  we  readily  see  that  the  farther  we  go  to  the  north  on 
the  earth,  the  longer  bodies  of  north  declination  remam  above  the 
horiioD,  and  the  more  quickly  those  of  south  declination  set.  In  the 
southern  hemisphere  Uie  reverse  is  true.  Thus,  in  the  month  of 
June,  when  the  sun  is  north  of  the  equator,  the  dnys  are  shortest 
near  the  aoath  pole,  and  contiDually  increase  in  length  as  we  go  north. 

Examples. 

(1).  On  April  »,  1879,  at  Washington,  the  altitude  of  Rigel  above 
the  west  hmuon  was  observed  to  be  12°  26'.    Ite  position  was : 

Right  ascension  =  S"  8-  44'-27  =  a. 
Declination  =  -  8°  20'  86'  =  «. 
The  latitude  of  Washington  is  +  88°  58'  89'  =  *. 
What  was  Uie  hour  angle  of  the  star,  and  the  sidereal  time  of  ob- 
servation f 

lgBina=       9-882478 

lg8in#=       9-797879 
lgsind=  -  9- 161681 

—  Ig  sin  ^  sin  S  =       8-959560 

-sin*sin.J=       0-091109 
sina=       0-215020 


sin  a  -  sin  f  sin  il  =       0806129 


Igcos^  = 
Igoos  o  = 

IgCOSf  008  d  = 

Ig  (ain  a  —  sin  ^  sin  d,  = 
Igcos  A  = 

*  -I- 1«  = 
sidereal  time  = 


9-891151 
9-995879 

9-886580 
9-486905 

9-599875  , 

66°  84'  88' 
4^  26'*  18'.90 
6*  8-44'.2T 
»k85»  2'.47 


(2)   Had  the  star  been  observed  at  the  same  altitude  in  the  east, 
iriut  would  have  been  the  sidereal  timet 
Ans.  a-A  =  0k4a-8«*.07. 


DBTBRMINATION  OF  LATITUDE. 


47 


Hence,  in  north- 
the  time  ftbove  the 
hemisphere,  f  and 

i  body  ifl  supposed 
)  greater  the  nega- 
I.  Cmisidering,  in 
on  and  north  and 
go  to  the  north  on 
I  remain  above  ths 
ination  set.  In  the 
,  in  the  month  of 
dnys  are  shortest 
^h  as  we  go  north. 


ude  of  Rigel  above 
position  was : 

=  a. 

iidereal  time  of  ob- 


J8' 
18'.90 

a'.47 

altitude  in  the  east, 


(8).  At  what  sidereal  time  does  Rigel  rise,  and  at  what  sidereal 
time  does  it  set  in  the  latitude  of  Washington  f 
-  tg«  -  -9-906728 
tgd  =  -  9166801 


cos  h  = 

A  = 

*  -5-  15  = 

a  ^ 


-  9  078029 

88^  12'  19" 
6h  82'»  49*.27 
5k    8»'44'.27 


rises  23''  8»"  aS'.OO 
sets  10<'  41"'  88*.fi4 

(4).  What  is  the  greatest  altitude  of  Rigel  above  the  horicon  of 
Washington,  and  what  is  its  greatest  depression  below  it  r  Ans. 
Altitude=4a'  46'  45" ;  depression =89°  26'  67'. 

(6).  What  is  the  greatest  altitude  of  a  ater  OD  the  equator  in  the 
meridian  of  Washington  f    Ans.  51°  •'  81".  _ 

(6).  The  ddcllnatron  of  the  pointer  in  the  Great  Bear  whioh  is 
nearest  the  pole  is  62'  80'  N.,  at  what  altitude  does  it  pass  abow 
the  pole  at  Washington,  and  at  what  altitude  does  it  pass  below  it  V 
Ans.  66°  88'  89'  above  the  pole,  and  11"  28'  »9'  when  below  it. 

(7).  If  the  declination  of  a  star  is  00°  N.,  what  length  of  sidereal 
time  is  it  above  the  horiaon  of  Washington  and  what  length  below  it 
during  its  apparent  diurnal  drauitf  Ans.  Above,  ai**  68"* ;  below. 
2''  S". 

§  8.  DETBBMIFATION   OF   lATTFUDBS    ON   THE 
BABTH  BY  ASTBONOlCKSAIi  OBSBBVATIONB. 

Latitude  fivm  eireumpolor  Uan.— In  Pig.  16  let  Z  represent  the 
zenith  of  the  place  of  observation,  P  the  pole,  and  MPZ  it  the  me- 
ridian, the  observer  bring  at  the 
centre  of  the  sphere.  Suppose 
.Sand  iS*  to  be  the  two  points 
at  which  a  oircumpolar  atar 
'  crosses  the  meridian  in  the  d*- 
scription  of  its  q>pannt  diurnal 
cn-bit  Then,  since  P  is  midway 
between  8  and  S", 
ZS  +  ZB       „„      .^ 


or. 


Z+Z' 


=  W-f. 


If,  then,  we  can  measure  tiie  dia- 
tances  Z  and  Z,  we  have 

Z4-Z^ 


Fie.  16. 


whidi  seeree  to  determine  f.    The  diataooes  ZmA  iF  can  be  m«M- 


,      ,.                .KS5^- 

fc " 

^SSy 

1 

48 

A8TnoyoMr. 

l!  ! 


nred  by  the  meridian  circle  or  the  sextant— both  of  which  instru- 
ments are  descrilied  in  the  next  chapter — and  the  latitude  in  then 
known.  Z  and  Z"  must  be  freed  from  tlie  effects  of  refraction.  In 
this  method  no  previous  knowledge  of  the  star's  declination  is  re- 
quired, provided  it  remains  constant  lietween  the  upper  and  lower 
transit,  which  is  the  case  for  fixed  stars. 

Latitude  by  Oiroum-ienith  Obaerratioiui If  two  stars 

8  and  S*,  whose  declinations  6  and  A'  are  known,  cross  the  meridian, 
one  north  and  the  other  south  of  the  xenith,  at  zenith  distances  Z  8 

and  ZS',  which  call  Z  and  Z',  and 
if  wo  have  measured  Z  and  Z,  we 
can  from  such  measures  find  the 
latitude ;  for  ^  =  d  +  Z  and  «  = 
<'  —  Z",  whence 

f  =  i((d  +  d')  +  (z-2r)]. 

It  will  be  noted  that  in  this  meth- 
od the  ktitude  depends  simply 
upon  the  mean  of  two  declinations 
which  ean  be  determined  before- 
hand, and  only  requires  the  diff'er- 
meg  of  Moith  distances  to  be  ac- 
curately measured,  while  the  aln 
solute  values  of  these  are  unknown.  In  this  oonslsts  its  capital  ad- 
vantage. This  is  the  method  invented  by  Oapt.  Amdrrw  Talcott, 
U.S.A.,  and  now  universally  adopted  in  America  in  Add  astronomy, 
in  the  practice  of  the  Coast  Survey,  etc. 

Latitude  liy  a  Single  Altitude  of  a  Star. — In  the  triangle 
ZPS(Vig.  14)thesidesareZP=iK)''~f;P5=90''  — a;  Z8  = 
Z  =  90"  —  ri ;  ZP8  =  A  =  the  hour  angle.  If  we  can  measure  at 
any  known  sidereal  time  0  the  altitude  a  of  the  star  iS,  and  if  we 
further  know  the  right  ascension,  a,  and  the  declination,  <i,  of  the 
body  (to  be  derived  from  the  Nftutical  Ahnanac  or  a  catalogue  uf 
•tan),  than  w«  have  fron  the  tritngle 

riofassinasind-l-cosacosdcosA; 
or,  idoM 

taeS-'  a;  da  f  ^tin  a  tin  6  +  CM  a  en  6  co»  (9  —  a), 

firaoi  whidi  wa  €M1  obtain  *.  It  to  to  be  noted  that  in  a  ptoce  whose 
latitode  if)  to  known,  this  observatimi  will  determine  9,  the  side- 
rsal  time,  ■•  explained  in  tha  last  sectiim;  if  the  sun  is  observed, 
t  to  aimiily  tiia  solar  tiua. 

Latftnde  tar  a  Meridian  Altttnde.— If  the  alUtode  of  the 
body  to  obaMTcd  on  tha  iMridiKD  and  south  of  the  lenith,  the  aqua- 
tton above beeonas,  since h^O'm thto case, 

idnfssin«sin4<fcosacos4, 
which  u  evidently  the  simplast  method  of  obtaining  f  fram  a 


or. 


J 


tSf. 


m^.Mi0^^mmm^^f^^m^^ 


l>oth  of  which  instru- 
«]  the  latitude  in  then 
ict8  of  refraction.  In 
tar's  declination  is  re- 
the  upper  and  lower 

btions.— If  two  stars 
rn,  cross  the  meridian, 
it  zenith  distances  Z  8 
hich  call  Z  and  Z',  and 
measured  Z  and  Z,  we 
ich  measures  find  the 
Dr  f  =  i  +  Z  and  «  = 
ence 

i  +  d')  +  (z-2r)]. 

9ted  that  in  this  meth- 
tud«  depends  simply 
san  of  two  declinations 
be  determined  before- 
nly  requires  the  diff'er- 
th  distances  to  be  ac- 
wmred,  while  the  ab- 
oonalsts  its  capital  ad- 
ipt.  Amdrrw  Talcovt, 
icain  Add  astronomy, 

Har. — In  the  triangle 
?S=90'  —  6i  Zti  = 
If  we  can  measure  at 
the  star  <t;,  and  if  we 
i  declination,  «i,  of  the 
nac  or  a  catalogue  uf 

I  cos  A; 

08  d  cos  (0  —  a), 

that  in  a  place  whoae 
cletermine  9,  the  side- 
the  sun  is  obaerred, 

f  the  altitude  of  the 
the  lenith,  the  equa- 


-a  +  S, 
kining  f  fram  a 


J 


PARALLAX. 


49 


ured  altitude  of  a  body  of  known  declination.  The  last  motliod  is 
that  commonly  used  at  sea,  the  altitude  iMiing  measured  by  the  sex- 
tant.   The  student  can  deduce  the  formula  for  a  northern  altitude. 


%  0.    PABALLAX  AND  8EMIDIAMBTEB. 

An  observation  of  the  apparent  poeition  of  a  heavenly 
body  can  give  only  the  direcUon  in  which  it  lies  from  the 
station  occupied  by  the  observer  without  any  direct  indi- 
cation of  the  distance.  It  is  evident  that  two  observers 
stationed  in  different  parts  of  the  earth  will  not  see  such 

tody  in  the  same  direction.    In  Fig.  18,  let  ^  be  a  sta- 


Fia  18.-«ABAU.AZ. 

tion  on  the  earth,  P  a  planet,  Z'  the  zenith  of  S,  and  the 
outer  arc  a  part  of  the  celestial  sphere.  An  observation 
of  the  apparent  right  ascension  and  declination  of  /*  taken 
from  the  station  1^  will  give  us  an  apparent  position  P*. 
A  similar  observation  at  8'  will  give  an  apparent  position 
P",  while  if  seen  from  the  centre  of  the  earth  the  appar- 
ent position  would  be  P,.  The  angles  P*  P  P,  and 
P*  P  P,^  which  represent  the  differences  of  direction,  are 
called  parallaaes.  It  is  clear  that  the  parallax  of  a  body 
depends  upon  its  distance  from  the  earth,  being  greater 
the  nearer  it  is  to  the  earth. 

The  word  parallaaB  having  several  distinct  applications, 
we  shall  give  them  in  order,  commeudug  with  the  most 
general  signification. 


« 


so 


ASTRONOMT. 


(1.)  In  itflmoHt  general  acceptation,  parallax  in  tlio  difTor- 
encu  between  the  diroctionH  of  a  l)ody  m  neeii  from  two 
different  standpoints.  This  difference  is  evidently  equal 
to  the  angle  made  between  two  lines,  one  drawn  from  each 
point  of  observation  to  the  body.  Thus  in  Fig.  18  the 
difference  between  the  direction  of  the  body  P  as  seen 
from  C  and  from  S'  is  equal  to  the  angle  P'  P  P^,  and  this 
again  is  equal  to  its  opposite  angle  SPG.  This  angle  is, 
however,  the  angle  between  the  two  points  C  and  S  as 
seen  from  P  :  we  may  therefore  refer  this  most  general 
deiinition  of  parallax  to  the  body  itself,  and  define  parallax 
as  the  angle  subtended  by  the  line  between  two  stations  as 
seen  from  a  heavenly  body. 

(2.)  In  a  more  restricted  sense,  one  of  the  two  stations  is 
supposed  to  be  some  centre  of  position  from  which  we 
imagine  the  body  to  be  viewed,  and  the  paralkx  is  the 
difference  between  the  direction  of  the  body  from  this 
centre  and  its  direction  from  some  other  point.  Thus 
the  parallax  of  which  we  have  just  spoken  is  the  differ- 
ence between  the  direction  of  the  body  as  seen  from  the 
centre  of  the  earth  G  and  from  a  point  on  its  surface  as  S. 
If  the  observer  at  any  station  on  the  earth  determines 
the  exact  direction  of  a  body,  the  parallax  of  which  we 
speak  is  the  correction  to  be  applied  to  that  direction  in 
order  to  reduce  it  to  what  it  would  have  been  had  the  ob- 
servation been  made  at  the  centre  of  the  earth.  Obser- 
vations made  at  different  points  on  the  earth's  surface  are 
compared  by  reducing  them  all  to  the  centre  of  the  earth. 

We  may  also  suppose  the  point  ^7  to  be  the  sun  and  the 
circle  /^  4^  to  be  the  earth's  orbit  around  it.  The  paral- 
lax will  then  be  the  difference  between  the  directions  of 
the  body  as  seen  from  the  earth  and  from  the  sun.  This 
is  termed  the  anmud  paraUatt,  because,  owing  to  the  an- 
nual revolution  of  the  earth,  it  goes  through  its  period 
in  a  year,  always  supposing  the  body  observed  to  be  at 
rest. 

(3.)  A  yet  more  restricted  parallax  is  the  horizontal 


lax  iR  t,he  diffor- 
Hceti  from  two 
ovidoutly  equal 
rewn  from  each 
in  Fig.  18  the 
ody  P  as  seen 
'PP,,  and  this 
This  angle  is, 
its  C  and  S  as 
is  most  general 
1  define  parallax 
two  stations  as 

B  two  stations  is 
From  which  we 
paralUx  is  the 
XKly  from  this 
r  point.  Thus 
nis  the  difFer- 
seen  from  the 
its  surface  as  S. 
rth  determines 
c  of  which  we 
lat  direction  in 
Ben  had  the  ob- 
earth.  Obser- 
•h's  surface  are 
re  of  the  earth. 
;he  sun  and  the 
t.  The  paral- 
e  directions  of 
the  sun.  This 
ving  to  the  an- 
>ugh  its  period 
served  to  be  at 

the  hmzoniai 


pahallax. 


51 


pavaJlm  of  a  hoavo.ilj  IkkIj.  The  parallax  first  doserilwl 
"1  the  last  pairugmpli  varies  with  the  jKwition  of  tlio  ob- 
■erveron  the  surface  of  the  earth,  and  lias  its  greatest 
value  when  the  body  is  seen  in  the  horizon  of  the  ob- 
server, as  may  be  seen  by  an  inspection  of  Fig.  19  in 
which  the  angle  GPS  attains  its  maximum  when  the  Hne 
18  IS  tangent  to  the  earth's  surface,  in  which  case  P 
will  appear  in  the  horizon  of  the  observer  at  8. 


IV.— HmunniTAi.  pAkaixax 

The  horizontal  parallax  depends  upon  the  distance  of  a 
body  m  the  followmg  manner:  In  the  triangle  C P 8. 
nght-angled  at  S,  we  have  S      ^  ^  ^. 

C8^GPmiCP8. 
If,  then,  we  put 

p,  the  radius  of  the  earth  G8\ 
JS^the  distance  of  the  body  P  from  the  centre  of  the 

»r,  the  angle  8P  G,  or  the  horizontal  parallax, 
we  shall  have, 

sin  n' 


P  =  r sin  >r;  r 


i«  It  wf  Tf"  *'  '''**  P^'^^^y  «P^«"«J'  the  quantity  p 
^^tabsolute  y  con^nt  for  aU  parts  of  thi  earth,  «7ito 
greatest  value  w  usually  taken  as  tiiat  to  which  4e  hori- 

r^  nt'  "^  ^  ^^«"^-  This  greatest  value  fa' « 
we  shall  hereafter  see,  the  radius  of  the  equator,  a^d  h" 


VS**" 


53  ARTRONOMT. 

corresponding  valnc  of  tho  parallax  18  thcroforo  called  the 
eqmiton'd  /wrhontaf  jMUuUfito). 

When  the  diatanco  /•  of  the  Ixxly  i»  known,  tho  wpxa- 
tonal  horizontal  parallax  can  bo  found  by  the  firet  of  the 
above  equationa  ;  when  tho  paralUx  can  be  obBerved,  the 
distance  r  is  found  from  the  second  equation.  IIow  this 
is  done  will  be  described  in  treating  the  subject  of  celes- 
tial measurement.  .  .  ,     .      ^  ,        ii„. 

It  is  easily  seen  that  the  equatorial  horizontal  parallax, 
or  the  angle  CPS^i'^  the  same  as  the  anguUr  seim- 
diameter  of  the  earth  seen  from  the  object  P.  In  fact, 
if  we  draw  the  Une  PST  tangent  to  «io  earth  at  ^,  he 
angle  5  P  5'  will  be  the  apparent  angular  diameter  of  tlie 
earth  as  seen  from  i>,  and  wiU  also  be  donblo  the  angle 
CP8  The  apparent  semi-diameter  of  a  heavenly  body 
is  therefore  given  by  the  same  f ormute  as  the  pindlax 
its  own  radius  being  substituted  for  that  of  the  earth.    If 

we  put, 
p,  the  radius  of  the  body  in  linear  measure  ; 
r,  the  distance  of  its  centre  from  the  observer,  expressed 

in  the  same  measure  ;  ^w.,„«r  • 

«,  its  anguhir  semi-diameter,  as  seen  by  the  observer  , 

we  shall  have, 

.    .      P 

sm  «  =  -• 

r 

If  we  measu^  tbe  semi-diameter  «,  and  know  the  dis- 
tance, r,  the  radius  of  the  body  will  be 

p  =  r  rin  «. 
Generally  tlie  angnkr  semi-diameters  of  the  heavenly 
bod^r.^L  small  that  they  may  be  considered  the  same 
^Wr^nl  We  may  theref  o.^  say  that  the  apparent 
Tn^Sr  diameter  of  a  heavenly  body  varies  inversely  as 
its  distance. 


oforo  called  the 

own,  the  cqua- 
the  first  of  the 
e  observed,  the 
ion.  IIow  thia 
iibject  of  celea- 

izontal  parallax, 
anffular  semi- 
set  P.  In  fact, 
earth  at  S',  the 
diameter  of  the 
onblo  the  angle 
a  heavenly  body 
as  the  parallax, 
if  the  earth.    If 

lure ; 

server,  expressed 

the  observer ; 


kd  know  the  dis- 


i  of  the  heavenly 
isidered  the  same 
th^the  apparent 
aries  inversely  as 


CHAPTER  II. 

ASTRONOMICAL  INSTRUMENTa 
§  1.    THE  EBFEAOmrO  TBLBSOOPB. 

In  explaining  the  theory  and  use  of  the  refracting  tele- 
scope,  we  shall  assume  that  the  reader  is  acquainted  with 
the  fundamental  principles  of  the  refraction  and  disper- 
sion of  light,  so  that  the  simple  enumeration   of  them 
will  recall  them  to  his  mind.     These  principles,  so  far 
as  we  have  occasion  to  refer  to  them,  are,   that  when 
a  ray  of  light  passing  through  a  vacuum  enters  a  trans- 
parent medium,  it  is  refracted  or  bent   from  its  course 
in  a  direction  toward  a  line   perpendicular  to  the  sur- 
face at  the  point  where  the  ray  enters ;  that  this  bend- 
ing follows  a  certain  law  known  as  the  law  of  sines ; 
that  when  a  pencil  of  rays  emanating  from  a  luminous 
point  falls  nearly  perpendicularly  upon  a  convex  lens, 
the  rays,  after  passing  through  it,  all  converge  toward  a 
point  on  the  other  side  called  a  focus  :  that  light  is  com- 
pounded of  rays  of  various  degrees  of  refrangibiUty,  so 
that,  when  thus  refracted,  the  component  rays  pursue 
slightly  different  courses,  and  in  passing  through  a  lens 
come  to  slightly  dififerent  foci ;  and  finally,  that  the  ap- 
parent angular  ma^itude  subtended  by  an  object  when 
viewed  from  any  point  is  inversely  proportional  to  its 
distance.* 

•  More  exactly.  In  the  cam  of  a  globe,  the  sine  of  the  angle  Is  in- 
venely  as  the  diatanoe  of  the  object,  aa  shown  on  the  preceding  page. 


t 


64  AHTRONOMY. 

We  ■hall  tint  doscrilM)  tho  toloncopo  in  its  siniplMt 
^H^^B  form,  showing  the  principluH  upon  whidi 
^^^^^1  its  action  depends,  leaving  out  of  considora- 
^^^^^1  tion  tlie  defects  of  aberration  which  retpiiro 
^l^^^l  special  devices  in  order  to  avoid  them.  In 
^^^^^1  the  simplest  fonn  in  which  we  can  conceive 
^^^^^1  ^  of  a  telescope,  it  consists  of  two  lenses  of 
^^^^H  §  unequal  focal  lengths.  The  puqKMBo  of  one 
^^^^^H  °  of  these  lenses  (called  the  of^ectivc,  or  object 
^^^^M  I  gkua)  is  to  bring  the  rays  of  light  from  a 
^^^^H  i  distant  object  at  which  the  telescope  is 
^^^^H  °  pointed,  to  a  focus  and  there  to  form  an 
^^^^H  ^  image  of  the  object.  The  purpose  of  the 
^^^^H  M  other  lens  (called  the  eye-piece)  is  to  view 
^^^^H  I  this  object,  or,  more  precisely,  to  form  an- 
^^^^^1  other  enlarged  image  of  it  on  the  retina  of 
^^^^^1  ^  tho 

^^^^H  §  The  figure  gives  a  representation  of  the 
^^^^H  I  course  of  one  pencil  of  the  rays  which  go  to 
^^^^H  S  fonn  the  image  ^  7'  of  an  object  /  li  after 
^^^^H  &  passing  through  the  objective  0  0'.  The 
"  pencil  chosen  is  that  composed  of  all  the 
rays  emanating  from  /  which  can  possibly 
[  „  fall  on  tho  objective  0  0'.  All  these  are, 
^^^^1  2  by  the  action  of  the  objective,  concentrated 
^^^^H  2  at  the  point  T.  In  the  same  way  each  point 
^^^^H  g  of  the  image  out  of  the  optical  axis  A  B 
^^^^H  %  emits  an  oblique  pencil  of  diverging  rays 
^^^^H  '.  which  are  made  to  converge  to  some  point 
^^^^1^.  of  the  image  by  the  lens.  The  image  of 
^^^^H£  the  point  B  of  the  object  is  the  point  A  of 
^^^^H  the  image.  We  must  conceive  the  image  of 
^^^^H  any  object  in  the  focus  of  any  lens  (or 
^^^^H  mirror)  to  be  formed  by  separate  bundles 
^^^^H  of  riiya  as  in  the  figure.  The  image  thus 
HHlB  formed  Inicomcs,  in  its  turn,  an  object  to 
be  viewed  by  the  eye-piece.     After  the  rays  meet  to  form 


I 


MAUNIFYIlfU  PVWh'Il  VF  TKI.K8G0PK. 


55 


in  ito  ninipleflt 
»luit  upon  which 
mi  of  conaidera- 
)n  which  recjuiro 
iivoid  them.  In 
wo  can  concoivo 
of  two  lunacH  of 
e  pur]K)8o  of  one 
hjective^  or  cijeot 
of  light  from  a 
the  telescope  is 
lere  to  form  an 
3  purpose  of  the 
•piece)  is  to  view 
jely,  to  form  an- 
on the  retina  of 

Mentation  of  the 
rays  which  go  to 
object  /  B  after 
jtivc  0  0'.  The 
ipoeed  of  all  the 
liich  can  poflBibly 
'.  All  these  are, 
;iye,  concentrated 
lie  way  each  point 
optical  axis  A  B 
)f  diverging  rays 
irge  to  some  point 
The  image  of 
ig  the  point  A  of 
leive  the  image  of 

of  any  lens  (or 
separate  bundles 

The  image  thus 
iim,  an  object  to 
rays  meet  to  form 


the  imago  (»f  an  object,  as  at  /,  thoy  continue  on  tlioir 
course,  diverging  from  /'  as  if  the  latter  wore  a  material 
object  reflecting  the  light.  There  is,  however,  this  excep- 
tion :  that  the  rays,  insteiwl  of  diverging  in  every  direction, 
only  fonn  a  small  cone  having  its  vertex  at  /',  and  having 
its  angle  equal  io  O  F  C  The  reason  of  this  is  that 
only  those  rays  which  pass  through  the  objective  can  form 
the  image,  and  thoy  must  continue  on  their  course  in 
straight  lines  after  forming  the  image.  This  image  can 
now  bo  viewed  by  a  lens,  or  even  by  the  unassisted  eye,  if 
the  observer  places  himself  behind  it  in  the  direction  A^ 
so  that  the  pencil  of  rays  shall  enter  his  eye.  For  the  pres- 
ent we  may  consider  the  eye-piece  as  a  simple  lens  of 
short  focus  nice  a  common  hand-magnifier,  a  more  com- 
plete description  l>«  ng  given  later. 

Magnifying  Fow«r.— To  unc^orstand  the  manner  in 
which  the  telescope  magnifies,  we  remark  that  if  an  eye  at 
the  object-glass  could  view  the  image,  it  would  appear  of 
the  saine  size  as  the  actual  objt^ct,  the  iii^ge  and  the  object 
subtending  the  same  angle,  but  lyinc^  »  opposite  direc- 
tion. This  angular  magnitude  beih^  ihe  same,  whatever 
the  focal  distance  at  which  •  >  ^  tmage  is  former',  it  follows 
that  the  size  of  the  inuige  vf  ties  iirectly  as  thu  local  length 
of  the  object-ghus.  But  when  we  view  an  object  with  a 
lens  of  small  focal  distance,  its  apparent  magnitude  is  thr; 
same  as  if  it  were  seen  at  that  focal  distance.  Consequently 
the  apparent  angular  magnitude  will  be  inversely  as  the 
focal  distance  of  the  leuF  Hence  the  focal  image  as 
seen  with  the  eye-pioce  will  appear  lai^r  than  it  would 
when  viewed  from  the  objective,  in  the  ratio  of  the  focal 
distance  of  the  objective  to  that  of  the  eye-piece.  But  we 
have  said  that,  seen  through  the  objective,  the  image  and 
the  real  object  subtend  the  same  angle.  Hence  the  angu- 
lar magnifyi^T  power  is  equal  to  the  focal  distance  of  the 
objective,  dir  h-]  by  that  of  the  eye-piece.  If  we  simply 
turn  the  telescope  end  for  end,  the  objective  becomes  the 
eye-piece  and  the  latter  the  objective.     The  ratio  is  in- 


66 


ASTRONOMY. 


verted,  and  the  object  is  diminished  in  size  in  tl:o  same 
ratio  that  it  is  increased  when  viewed  in  the  ordinary 
way.  If  we  should  form  a  telescope  of  two  lenses  of 
equal  focal  length,  by  placing  them  at  double  their  focal 
distance,  it  would  not  magnify  at  all. 

The  image  formed  by  a  convex  lens,  being  upside 
down,  and  appearing  in  the  same  position  when  viewed 
with  the  eye-piece,  it  follows  that  the  telescope,  when 
constructed  in  the  simplest  manner,  shows  all  objects  in- 
verted, or  upside  down,  and  right  side  left.  This  is  the 
case  with  all  refracting  telescopes  made  for  astronomical 
uses. 

Light-gathering  Power.— It  is  not  merely  by  magnify- 
ing that  the  telescope  assists  the  vision,  but  also  by  in- 
creasing the  quantity  of  light  which  reaches  the  eye  from 
the  object  at  which  we  look.  Indeed,  should  we  view  an 
object  through  an  instrument  which  magnified,  but  did 
not  increase  the  amount  of  light  received  by  the  eye,  it  is 
evident  that  the  brilliancy  would  be  diminished  in  propor- 
tion as  the  surface  of  the  object  was  enlarged,  since  a  con- 
stant amount  of  light  would  be  spread  over  an  increased 
surface  ;  and  thus,  unless  the  light  were  faint,  the  object 
might  become  so  darkened  as  to  be  less  plainly  seen  tlian 
with  the  naked  eye.  How  the  telescope  increases  the 
quantity  of  light  will  be  seen  by  considering  that  when  the 
unaided  eye  looks  at  any  object,  the  retina  can  only  re- 
ceive  so  many  rays  as  fall  upon  the  pupil  of  the  eye.  By 
the  use  of  the  telescope,  it  is  evident  that  ac  many  rays 
can  be  brought  to  the  retina  as  fall  on  the  entire  object- 
glass.  Tlie  pupil  of  the  human  eye,  in  its  normal  state, 
has  a  diameter  of  about  one  fifth  of  an  inch  ;  and  by  the 
use  of  the  telescope  it  is  virtually  increased  in  surface  in 
the  ratio  of  the  square  of  the  diameter  of  the  objective  to 
the  square  of  one  fifth  of  an  inch.  Thus,  with  a  two-mch 
aperture  to  our  telescope,  the  number  of  rays  collected  is 
one  Imndred  times  as  great  as  the  number  collected  with 
the  naked  eye.  , 


1 


ze  in  tlio  Batne 
the  ordinary 
two  lenses  of 
ible  their  focal 


Q 


being  upside 
when  viewed 
elescope,  when 
all  objects  in- 
t.  This  is  the 
or  astronomical 

sly  by  magnify- 
but  also  by  in- 
hs  the  eye  from 
uld  we  view  an 
!;niiied,  but  did 
by  the  eye,  it  is 
shed  in  propor- 
:ed,  since  a  con- 
er  an  increased 
faint,  the  object 
lainly  seen  tiian 
e  increases  the 
g  that  when  the 
na  can  only  re- 
»f  the  eye.  By 
t  ac  many  rays 
le  entire  object- 
B  normal  state, 
ch  ;  and  by  the 
d  in  surface  in 
th&  objective  to 
with  a  two-inch 
ays  collected  is 
r  collected  with 


POWER  OF  TELESCOPE. 
"With  a  5-inch  object-glass,  the  ratio  is 

((       in     (<  (t  ((  ((         (( 

n         ii^g      ((  <t  ((  ((  (( 

i(     20    "        ''  "         "       " 

((     26    "        '*  *'         **       ** 


67 


625  to  1 

2,500  to  1 

5,625  to  1 

10,000  to  1 

16,900  to  1 


When  a  minute  object,  like  a  star,  is  viewed,  it  is 
necessary  that  a  certain  number  of  rays  should  fall  on  the 
retina  in  order  that  the  star  may  be  visible  at  all.  It  is 
therefore  plain  that  the  use  of  the  telescope  enables  an 
observer  to  see  much  fainter  stars  than  he  could  detect 
with  the  naked  eye,  and  also  to  see  faint  objects  much 
better  than  by  unaided  vision  alone.  Thus,  with  a  26- 
inch  telracope  we  may  see  stars  so  minute  that  it  would 
require  many  thousands  to  be  visible  to  the  unaided  eye. 

An  important  remark  is,  however,  to  be  made  here, 
inspecting  Fig.  20  we  see  that  the  cone  of  rays  passing 
through  the  objiBct-glass  converges  to  a  focus,  then  diverges 
at  the  same  angle  in  order  to  pass  through  the  e/e-piece. 
After  this  passaga  the  rays  emerge  from  the  eye-piece 
parallel,  as  shown  in  Fig.  22.  It  is  evident  that  the 
diameter  of  this  cylinder  of  parallel  rays,  or  '*  emergent 
pencil,"  as  it  is  called,  is  less  than  the  diameter  of  the 
object-glass,  in  the  same  ratio  that  the  focal  length  of  the 
eye-piece  is  less  than  that  of  the  object-glass.  For  the 
central  ray  //'is  the  common  axis  of  two  cones,  A 1'  and 
0  r  Cfj  having  the  same  angle,  and  equal,  in  length  to 
the  respective  focal  distances  of  the  glasses.  But  this 
ratio  is  alsb  the  nutgnifying  power.  Hence  the  diameter 
of  the  emergent  pencil  of  rays  is  found  by  dividing  the 
diameter  of  the  object-glass  by  the  magnifying  power. 
Now  it  is  clear  that  if  the  magnifying  power  is  so  small 
that  this  emergent  pencil  is  larger  than  the  pupil  of  the 
eye,  all  the  light  which  falls  on  the  object-glass  cannot 
enter  the  pupil.  This  will  be  the  case  whenever  the 
magnifying  power  is  less  than  five  for  every  inch  of 
aperture  of  the  glass.    If,  for  example,  the  observer  should 


58 


ASTBONOMT. 


look  through  a  twelve-inch  telescope  with  an  eye-piece 
so  large  that  the  magnifying  power  was  only  30,  the 
emergent  pencil  would  be  two  fifths  of  an  inch  in  diam- 
eter, and  only  so  much  of  the  light  could  enter  the  pupil 
as  fell  on  the  central  six  inches  of  the  object-glass. 
Practically,  therefore,  the  observer  would  only  be  using  a 
six-inch  telescope,  all  the  light  which  fell  outside  of  the 
six-inch  circle  being  lost.  In  order,  therefore,  that  he 
may  get  the  advantage  of  all  his  object-glass,  he  must  use 
a  magnifying  power  at  least  five  times  the  diameter  of  his 
objective  in  inches. 

When  the  magnifying  power  is  carried  beyond  this 
limit,  the  action  of  a  telescope  will  depend  partly  on  the 
nature  of  the  object  one  is  looking  at.  Viewing  a  star, 
the  increase  of  power  will  give  no  increase  of  light,  and 
therefore  no  increase  in  the  apparent  brightness  of  the 
star.  If  one  is  looking  at  an  object  having  a  sensible 
surface,  as  the  moon,  or  a  planet,  the  light  coming 
from  a  given  portion  of  the  surface  will  be  spread  over  a 
larger  portion  of  the  retina,  as  the  magnifying  power 
is  increased.  All  magnifying  must  then  be  gained  at 
the  expense  of  the  apparent  illumination  of  the  surface. 
Whether  this  loss  of  illumination  is  important  or  not  will 
depend  entirely  on  how  much  light  is  to  spare.  In  a 
general  way  we  may  say  that  the  moon  and  all  the  plan- 
ets nearer  than  Saturn  are  so  brilliantly  illuminated  by 
the  sun  that  the  magnifying  power  can  be  carried  many 
times  above  the  limit  without  any  loss  in  the  distinctness 
of  vision. 

The  Telescope  in  Meaaurement. — A  telescope  is  gen- 
erally thought  of  only  as  an  instrument  to  assist  the  eye 
by  its  magnifying  and  light-gathering  power  in  the  man- 
ner we  have  described.  But  it  has  a  very  important 
additional  function  in  astronomical  measurements  by  en- 
abling the  astronomer  to  point  at  a  celestial  object  with  a 
certainty  and  accuracy  otherwise  unattainable.  This  func- 
tion of  the  telescope  was  not  recognized  for  mon  than 


USE  OF  TELBSCOPK 


59 


ith  an  eye-piece 
as  only  30,  the 
m  inch  in  diam- 
.  enter  the  pupil 
the  object-glass. 

I  only  be  using  a 

II  outside  of  the 
lerefore,  that  he 
^ass,  he  must  use 
}  diameter  of  his 

ed  beyond  this 
id  partly  on  the 
Viewing  a  star, 
se  of  light,  and 
rightness  of  the 
Eiving  a  sensible 
e  light   coming 
be  spread  over  a 
ignifying  power 
in  be  gained  at 
of  the  surface, 
rtant  or  not  will 
to  spare.     In  a 
uid  all  the  plan- 
illuminated  by 
)e  carried  many 
the  distinctness 

elescope  is  gen- 
to  assist  the  eye 
wer  in  the  man- 
very  important 
arements  by  en- 
ial  object  with  a 
t>le.  This  fonc- 
l  for  more  thaa 


^^m^^m 


half  a  century  after  its  invention,  and  after  a  long  and 
rather  acrimonious  contest  between  two  schools  of  astron- 
omers. Until  the  middle  of  the  seventeenth  century, 
when  an  astronomer  wished  to  determine  the  altitude  of  a 
celestial  object,  or  to  measure  the  angular  distance  be- 
tween two  stars,  he  was  obliged  to  point  his  quadrant  or 
other  measuring  instrument  at  the  object  by  means  of 
'  *  pinnules. ' '  These  served  the  same  purpose  as  the  sights 
on  a  rifle.  In  using  them,  however,  a  difliculty  arose. 
It  was  impossible  for  the  observer  to  have  distinct  vision 
both  of  the  object  and  of  the  pinnules  at  the  same  time, 
because  when  the  eye  was  focused  on  either  pinnule,  or 
on  the  object,  it  was  necessarily  out  of  focus  for  the 
others.  The  only  way  to  diminish  this  diflSculty  was  to 
lengthen  the  arm  on  which  the  pinnules  were  fastened  so 
that  the  latter  should  be  as  far  apart  as  possible.  Thus 
Tycho  Bbahe,  before  the  year  1600,  had  measuring  in- 
struments very  much  larger  than  any  in  use  at  the  pres- 
ent time.  But  this  plan  only  diminished  the  difficulty  and 
could  not  entirely  't)bviate  it,  because  to  be  manageable 
the  instrument  must  not  be  very  large. 

About  1670  the  English  and  French  astronomers  found 
that  by  simply  inserting  fine  threads  or  wires  exactly  in 
the  focus  of  the  telescope,  and  then  pointing  it  at  the  ob- 
ject, the  image  of  that  object  formed  in  the  focus  could  be 
made  to  coincide  irith  the  threads,  so  that  the  observer 
could  see  the  two  exactly  superimposed  upon  each  other. 
"When  thus  brought  into  coincidence,  it  was  known  that 
the  point  of  the  object  on  which  the  wires  were  set  was  in 
a  straight  line  passing  through  the  wires,  and  through  the 
centre  of  the  object-glass.  So  exactly  could  such  a  pointr 
ing  be  made,  that  if  the  telescope  did  not  magnify  at  all 
(the  eye-piece  and  object-glass  being  of  equal  focal  length), 
a  very  important  advance  would  still  be  made  in  the  ac- 
curacy of  astronomical  measurements.  This  line,  passing 
oentrally  through  the  telescope,  we  call  the  line  of  col- 
Umatim  of  the  telescope,  A  Bin  Fig.  20.     If  we  have 


sifiEBisiasjc;; 


IfSJ^WftffS 


flO 


A8TB0N0MT. 


any  way  of  determining  it  we  at  once  realize  the  idea  ex- 
pressed in  the  opening  chapter  of  this  book,  of  a  pencil  ex- 
tended in  a  definite  direction  from  the  earth  to  the  heav- 
ens. If  the  observer  simply  sets  his  telescope  in  a  fixed 
position,  looks  through  it  and  notices  what  stars  pass  along 
the  threads  in  the  eye-piece,  he  knows  that  those  stars  all 
lie  in  the  line  of  collimation  of  his  telescope  at  that  instant. 
By  the  diurnal  motion,  a  pencil-mark,  as  it  were,  is  thus 
being  made  in  the  heavens,  the  direction  of  which  can  be 
determ'ned  with  far  greater  precision  than  by  any  meas- 
urements with  the  unaided  eye.  The  direction  of  this  line 
of  collimation  can  be  determined  by  methods  which  we 
need  not  now  describe  in  detail. 

The  Aohromatio  Telescope. — The  simple  form  of  tele- 
scope which  we  have  described  is  rather  a  geometrical 
conception  than  an  actual  instrument.  Only  the  earli- 
est instruments  of  this  class  were  made  with  so  few  as  two 
lenses.  Galileo's  telescope  was  not  made  in  the  form 
which  we  have  described,  for  instead  of  two  convex  lenses 
having  a  common  focus,  the  eye-piece  was  concave,  and 
was  placed  at  the  proper  distance  inside  of  the  focus  of  the 
objective.  This  form  of  instrument  is  still  used  in  opera- 
glasses,  but  is  objectionable  in  large  instruments,  owing  to 
the  smallness  of  the  field  of  view.  The  use  of  two  con- 
vex lenses  was,  we  believe,  first  proposed  by  Eepleb. 
Although  telescopes  of  this  simple  form  were  wonderful 
instruments  in  their  day,  yet  they  would  not  now  be  re- 
garded as  serving  any  of  the  purposes  of  such  an  instru- 
ment, owing  to  the  aberrations  with  which  a  single  lens  is 
effected.  We  know  that  when  ordinary  light  passes 
through  a  simple  lens  it  is  partially  decomposed,  the  differ- 
ent rays  coming  to  a  focus  at  different  distances.  The 
focus  for  red  rays  is  most  distant  from  the  object-glass, 
and  that  for  violet  rays  the  nearest  to  it.  Thus  arises 
the  ohromatio  aberration,  of  a  lens.  But  this  is  not  all. 
Even  if  the  light  is  but  of  a  single  degree  of  refrangi- 
bility,  if  the  surfaces  of  our  lens  are  spherical,  the  rays 


I? 


ize  the  idea  ex- 
,  of  a  pencil  ex- 
■th  to  the  hear- 
scope  in  a  fixed 
stars  pass  along 
it  those  stars  all 
B  at  that  instant, 
it  were,  is  thus 
>f  which  can  be 
in  by  any  meas- 
tion  of  this  line 
ithods  which  we 

le  form  of  tele- 
r  a  geometrical 
Only  the  earli- 
th  so  few  as  two 
ide  in  the  form 
leo  convex  lenses 
as  concave,  and 
'  the  focus  of  the 
11  used  in  opera- 
Lments,  owing  to 
use  of  two  con- 
led  by  Kepleb. 
were  wonderful 
not  now  be  re^ 
such  an  instru- 
li  a  single  lens  is 
17  light  passes 
)0fled,  the  differ- 
distances.  The 
the  object-glass, 
it.  Thus  arises 
t  this  is  not  all. 
;ree  of  refrangi- 
herical,  the  rays 


A  CHROMA  TIO  OBJECT-  GLASS. 


61 


wliich  pass  near  the  edge  will  come  to  a  shorter  focus 
than  those  which  pass  near  the  centre.  Thus  arises 
spherical  aherratian.  This  aberration  might  be  avoided 
if  lenses  could  be  ground  with  a  proper  gradation  of 
curvature  from  the  centre  to  the  circumference.  Prac- 
tically, however,  this  is  impossible  ;  the  deviation  from 
imiform  sphericity,  which  an  optician  can  produce,  is  too 
small  to  neutralize  the  defect. 

Of  these  two  defects,  the  chromatic  aberration  is  much 
the  more  serious  ;  and  no  way  of  avoiding  it  was  known 
until  the  latter  part  of  the  last  century.  The  fact  had, 
indeed,  been  recognized  by  mathematicians  and  physicists, 
that  if  two  glasses  could  bo  found  having  very  different 
ratios  of  refractive  to  dispersive  powers,*  the  defect  could 
be  cured  by  combining  lenses  made  of  these  different 
kinds  of  glass.  But  this  idea  was  not  realized  until  the 
time  of  DoLLOND,  an  English  optician  who  lived  during 
the  last  century.  This  artist  found  that  a  concave  lens  of 
flint  glaj98  could  be  combined  with  a  convex  lens  of  crown  of 
double  the  curvature  in  such  a  manner  that  the  dispersive 
powers  of  the  two  lenses  should  neutralize  each  other,  being 
equal  and  acting  in  opposite  di- 
rections. But  the  crown  glass 
having  the  greater  refractive 
power,  owing  to  its  greater  cur- 
vature, the  rays  would  be  brought 
to  a  focus  without  dispersion. 
Such  is  the  construction  of  the 
achromatic  objective.  As  now 
made,  the  outer  or  crown  glass  lens  is  double  convex  ;  tlie 
inner  or  flint  one  is  generally  nearly  plano-concave. 
Fig.  31  shows  ihe  section  of  such  an  objective  as  made 
by  Alvan  Glabk  &  Sons,  the  inner  curves  of  the  crown 
and  flint  being  nearly  equal. 

*  By  the  r^fraelitie  power  of  a  glass  is  meant  its  power  of  bending  the 
rays  out  of  thefar  ooane,  so  as  to  bring  them  tn  a  focus.  By  its  d^pvr- 
«iw  potter  is  meant  its  power  (rf  separating  tlie  colors  so  as  to  form  a 
Vectnun,  or  to  produce  chromatic  aberration. 


iiiiiiiriii 


Fio. 


21.— flBonoN  or  oBntoT- 
ahim. 


ms.:-^^ 


aX-^ 


mmm 


63 


ASTRONOMY. 


^\ 


A  great  advantage  of  the  achromatic  objective  is  that  it 
may  be  made  to  correct  the  spherical  as  well  as  the  chro- 
matic aberration.  This  is  effected  by  giving  the  proper 
curvature  to  the  various  surfaces,  and  by  making  such 
slight  deviations  from  perfect  sphericity  that  rays  passing 
through  all  parts  of  the  glass  shall  come  to  the  same  focus. 

The  Secondary  Speotrum. — It  ia  now  known  that  the 
chromatic  aberration  of  an  objective  cannot  be  perfectly 
corrected  with  any  combination  of  glasses  yet  discovered. 
In  the  best  telescopes  the  brightest  rays  of  the  spectrum, 
which  are  the  yellow  and  green  ones,  are  all  brought  to 
the  same  focus,  but  the  red  and  bine  ones  reach  a  focus 
a  little  farther  from  the  objective,  and  the  violet  ones  a 
focus  still  farther.  Hence,  if  we  look  at  a  bright  star 
through  a  large  telescope,  it  will  be  seen  surrounded  by  a 
blue  or  violet  light.  If  we  push  the  eye-piece  in  a  little 
the  enlarged  image  of  the  star  will  be  yellow  in  the  centre 
and  purple  around  the  border.  This  separation  of  colors 
by  a  pair  of  lenses  is  called  a  secondary  spectrum. 

Bye-Pleoe.— In  the  skeleton  form  of  telescope  before 
described  the  eye-piece  as  well  as  the  objective  was  con- 
sidered as  consisting  of  but  a  single  lens.  But  with  such 
an  eye-piece  vision  is  imperfect,  except  in  the  centre  of 
the  field,  from  the  fact  that  the  image  does  not  throw 
rays  in  every  direction,  but  only  in  straight  lines  away 
from  the  objective.  Hence,  the  rays  from  near  the  edges 
of  the  focal  image  fall  on  or  near  the  edge  of  the  eye- 
piece, whence  arises  distortion  of  the  image  formed  on 
the  retina,  and  loss  of  light.  To  remedy  this  difficulty  a 
lens  is  inserted  at  or  very  near  the  place  where  the  focal 
image  is  formed,  for  the  purpose  of  throwmg  the  different 
pencils  of  rays  which  emanate  from  the  several  parts  of 
the  image  toward  the  axis  of  the  telescope,  so  that  they 
shall  all  paos  nearly  through  the  centre  of  the  eye  lens  pro- 
per. These  two  lenses  i>re  together  called  the  eye-piece. 
There  are  some  small  differences  of  detail  in  the  con- 
struction of  eye-pieces,  but  the  general  principle  is  the 


J 


TUEOnr  OF  OBJBXfT-OLASS. 


ictive  is  that  it 
11  as  the  chro- 
ng  the  proper 

making  Bnch 
it  rays  passing 
he  same  focus. 
noMOi  that  the 
)t  be  perfectly 
yet  discovered. 
'  the  spectrum, 
>  all  brought  to 
s  reach  a  focus 
le  violet  ones  a 
t  a  bright  star 
arrounded  by  a 
piece  in  a  little 
w  in  the  centre 
ration  of  colors 
iotntm. 

elescope  before 
jective  was  con- 
But  with  such 
1  the  centre  of 
loes  not  throw 
ght  lines  away 
L  near  the  edges 
Jge  of  the  eye- 
lage  formed  on 
this  difficulty  a 
gvhere  the  focal 
ug  the  different 
several  parts  of 
36,  so  that  they 
the  eye  lens  pro- 

the  eye-piece. 
»il  in  the  con- 
principle  is  die 


same  in  all.  The  two  recognized  classes  are  tlio  posi- 
tive and  negative,  the  former  being  those  in  which  the 
imago  is  formed  before  the  light  reaches  the  field  lens  ;  the 
negative  those  in  wlilch  it  is  fonned  between  the  lenses. 

The  figure  shows  the  positive  eye-pieco  drawn  accurately  to  scale. 
0  /  is  one  of  the  converging;  pencils  from  the  object-glass  which 
forms  one  point  (/)  of  the  focal  image  /  a.  This  image  is  viewed 
by  the  Jlela  lent  F  of  the  eye-piece  as  a  real  object,  and  the  shaded 
pencil  between  F  and  E  shows  the  course  of  these  rays  after  de- 
viation by  F.  If  there  were  no  eye-lmu  E  an  eye  properly  placed 
beyond  F  would  see  an  ima^  at  /'  a'.  The  eye-lens  E  receives  the 
pencil  of  rays,  and  deviates  it  to  the  observer's  eye  placed  at  such  a 
point  that  the  whole  incident  pencil  will  pass  through  the  pupil 
and  fall  on  the  retina,  and  thus  be  effective.    As  we  saw  in  the 


22.— BBcnoR  or  a  vaarmt  BTR-pmnL 


figure  of  the  refracting  telescope,  ever;  point  of  the  object  producet 

a  pencil  similar  to  0  /,  and  the  whole  surfaces  of  the  lensea  F 

and  E  are  covered  with  rays.    All  of  these  pencils  paasinK  through 

the  pupil  ^  to  make  up  the  retinal  image.    This  image  u  refemd 

by  the  mind  to  the  distance  of  distinct  vision  (about  ten  inches), 

and  the  image  A  I"  represents  the  dimension  of  the  final  image 

A  F' 
relative  to  the  image  a  /  as  fonned  by  the  objective  and  — y  ^ 

evidently  the  nujipiif ving  power  of  this  particular  eye-piece  used 
in  combination  with  this  particular  objective. 

More  Eicaot  Theory  of  the  Ol^jeotive For  the  benefit  of  the 

reader  who  wishes  a  more  precise  knowledge  of  the  optical  princi- 

Sles  on  which  the  action  of  the  objective  or  other  system  of  lenses 
epends,  we  present  the  following  geometrical  theory  of  the  sub- 
ject. This  theory  ft  not  rigidly  exact,  but  is  sufficiently  so  for  all 
ordinary  computations  of  we  focal  lengths  and  sizes  of  image  in 
the  usual  combinations  of  lenses. 


1 


IV 


64 


A8TR0N0MY. 


Oentrea  of  Oonyenenoe  and  Divergenoe.—Siinpoge  A  B,  Fig. 
28,  to  be  a  IcnH  or  commnation  of  lonscs  on  which  the  light  falls  from 
the  left  hand  and  passes  through  to  the  right.  Suppose  rays  parallel 
to  7?  P  to  fall  on  every  part  of  the  first  surface  of  tnc  glass.  After 
passing  through  it  they  are  all  supposed  to  converge  nearly  or  ex- 
actly to  the  same  point  If.  Among  all  these  rays  there  is  one,  and 
one  only,  the  course  of  which,  after  emerging  from  the  glass  at  Q, 
will  be  parallel  to  its  original  direction  It  P.  Let  li  P  Qlf  be  this 
central  ray,  which  will  \hs  completely  determined  by  the  direction 
from  which  it  comes.  Next,  let  m  take  a  ray  coming  from  another 
direction  m  8  P,  Among  all  the  rays  parallel  to  8  P,  let  us  take 
that  one  which,  after  emerging  from  the  glass  at  7*,  moves  in  a  line 
parallel  to  its  original  direction.  Continuing  the  process,  let  u> 
suppose  isolated  rays  coming  from  all  parts  of  a  distant  object  sub- 
ject to  the  single  condition  that  the  course  of  each,  after  passing 
through  the  glus  or  system  of  glasses,  shall  be  parallel  to  its  original 
course.  These  rays  we  may  call  cmtml  rayt.  They  have  this  re- 
markable property,  pointed  out  by  Oauw:  that  they  all  converge 


Fig.  38. 

toward  a  single  point,  i*,  in  coming  to  the  gloss,  and  diverge  from 
another  point,  i*,  after  passing  through  the  last  lens.  These  points 
were  termed  by  Gacbs  "  Hauptpunkte,"  or  principal  points.  But 
they  will  probably  be  better  understood  if  we  call  the  first  one  the 
centre  of  convergence,  and  the  second  the  centre  of  divergence. 
It  must  not  be  understood  that  the  central  rays  necessarily  pass 
through  these  centres.  If  one  of  them  lies  outside  the  first  or  lost 
refracting  surface,  then  the  central  rays  must  actually  pass  through 
it.  But  if  they  lie  between  the  surfaces,  they  will  be  fixed  by  the 
continuation  of  the  straight  line  in  which  the  rays  move,  the  latter 
being  refracted  out  of  their  course  by  passing  through  the  surface, 
and  thus  avoiding  the  points  in  question.  If  the  lens  or  system  of 
lenses  be  turned  around,  or  if  the  light  passes  through  them  in  an 
opposite  direction,  the  centre  of  oonveigence  in  the  first  case  be- 
comes the  centre  of  divergence  in  the  second,  and  mee  verta.  The 
necessity  of  this  will  be  clearly  seen  by  reflecting  that  a  return  ray 
of  light  will  always  keep  on  the  course  of  the  original  ray  in  the 
opposite  direction. 


liinpoBe  A  B,  Fig. 
ic  light  falls  from 
iposc  rays  parallel 
the  glass.  After 
rge  nearly  or  ex- 
tnere  is  one,  and 
n  the  glass  at  Q, 
R  P  Q  li' he  Mh 
{ by  the  direction 
ling  from  another 
0  SP,  let  us  take 
T,  moves  in  a  line 
he  process,  let  us 
istant  object  sub- 
ich,  after  passing 
illcl  to  its  original 
hey  have  this  re- 
they  all  converge 


and  diverge  from 
lens.  These  points 
cipal  points.  But 
11  the  first  one  the 
tre  of  divergence. 
j»  necessarily  pass 
ide  the  first  or  last 
dually  pass  through 
rill  be  fixed  by  the 
lys  move,  the  latter 
irough  the  surface, 
le  lens  or  system  of 
hrough  them  in  an 
n  the  first  case  be- 
tnd  mce  verta.  The 
ig  that  a  return  ray 
I  original  ray  in  the 


riiKOBY  OF  oBJBcr-aLAaa. 


65 


The  figure  represents  a  plano-convex  lenn  with  light  falling  on 
the  convex  side.     In  this  case  the  centre  of  convergence  will  be 
the  convex  surface,  and  that  of  divergence  inside  the  glass 


on 


aliout  one  third  or  two  fifths  of  the  way  from  the  convex  to  the 
plane  surface,  the  positions  varying  with  the  refractive  index  of  the 
glass.  In  a  double  convex  lens,  both  points  will  lie  inside  the  glass, 
while  if  a  glass  is  concave  on  one  side  and  convex  on  the  other, 
<  ne  of  the  points  will  be  outside  the  glass  on  the  concave  side.  It 
nust  be  remembered  that  the  positions  of  these  centres  of  conver- 
gance  and  divergence  depend  solely  on  the  form  and  size  of  the 
lenses  and  their  refractive  indices,  and  do  not  refer  in  any  way  to 
the  distances  of  the  objects  whose  images  the^  form. 

Tht  principal  properties  of  a  lens  or  objocti^  c,  by  which  the  size 
of  imageb  «re  determined,  are  as  follows  :  Since  the  angle  9  P  B! 
made  by  the  u>erging  rays  is  equal  U>  RP  8,  made  by  the  con- 
verging ones,  it  fo;Ws,  that  if  a  lens  form  the  image  of  an  object, 
the  size  of  the  image  will  be  to  that  of  the  object  as  their  respec- 
tive distances  from  the  cei:t<««  of  convergence  and  divergence.  In 
other  words,  the  object  seen  from  the  centre  of  convergence  P  will 
be  of  the  same  angular  magnitude  as  the  image  seen  from  the 
centre  of  divergence  P*. 

By  eotyugaU  fon  of  a  lens  or  system  of  lenses  we  mean  a  puIi-  of 
points  such  that  if  rays  diverge  from  the  one,  they  will  converge  to 
the  other.  Hence  if  an  object  is  in  one  of  a  pair  of  such  foci,  the 
image  will  be  formed  in  the  ot)i«r. 

By  the  rtfraOMt  powr  of  a  lens  or  combination  of  lenses,  we 
mean  its  influence  in  refracting  parallel  rays  to  a  focus  which  we 
may  measure  by  the  recipiocai  of  its  focal  distaoce  or  1  -i-f.  Thus, 
the  power  of  a  piece  of  plain  glass  is  0,  because  it  cannot  bring 
rays  to  a  focus  at  alL  The  power  of  a  convex  lens  is  positive,  while 
that  of  a  concave  lens  is  negative.  In  the  latter  case,  it  will  be 
remembered  by  the  student  of  optics  that  the  virtual  focus  is  on 
the  same  side  of  the  lens  from  which  the  rays  proceed.  It  is  to 
be  noted  that  when  we  speak  of  the  focal  distance  of  a  lens,  we 
mean  the  distance  from  the  centre  of  diveq^nce  to  the  focus  for 
])arallel  rays.  In  astronomical  language  this  focus  is  called  the 
stelhir  focus,  being  that  for  celestial  objects,  all  of  which  we  may 
regard  as  infinitely  distant.    If,  now,  we  put 

p,  the  power  of  the  lens ; 

/,  its  stellar  focal  distance ; 

fy  the  distance  of  an  object  from  the  centre  of  convergence ; . 

/',  the  distance  of  its  image  from  the  centre  of  divergence ;  then 
the  equation  which  determines/ will  be 

1       1       1 


f^f'-f-^' 


or. 


f-  ffL. . 


/'  =  >^. 


f-f 

From  these  equations  may  be  found  the  focal  length,  having  the 
distance  at  which  the  image  of  an  object  is  formed,  or  viee  verta. 


?*?»*« 


wfsMTfmi'^m**- , 


11 


06 


ASTRONOMY. 


8  9.    BSFLEOTDfO  TXLBBOOPBS. 

Ar  wo  liavo  Been,  the  most  enential  part  of  a  rafraeting 
teluHcopo  is  the  objective,  which  brings  all  the  incident 
rays  from  an  object  tu  one  focus,  forming  there  an  image 
of  tba  object.  In  reflecting  telescopes  (reflectors)  the 
objective  is  a  m^ror  of  speculum  metal  or  silvered  glass 
ground  tQ  the  shape  of  a  paraboloid.  The  figure  shoMnt 
the  action  of  such  a  mirroi  on  a  bundle  of  parallel  rays, 
which,  after  impinging  on  it,  are  brought  by  reflection  tu 
one  focus  F.  The  image  formed  at  this  focus  may  be 
viewed  with  an  eye-piece,  as  in  the  case  of  the  refracting 
telescope. 

The  eye-pieces  used  with  such  a  mirror  are  of  the  kinds 
already  described.     In  the  figure  the  eye-piece  would 


FlO.  84.— CONCAVS  MIRBOR  rORMINO  AK  IMAOC 


have  to  be  placed  to  the  right  of  the  point  F,  and  the 
observer's  head  would  thus  interfere  with  the  incident 
light.  Various  devices  have  been  proposed  to  remedy  this 
inconvenience,  of  which  we  will  ifaiiffribe  the  two  most 
common. 

Hm  Vewtonieii  IMeecope. — In  this  form  the  rays  of 
light  reflected  from  the  mirror  are  made  to  fall  on  a  small 
plane  mirror  placed  diagonally  just  before  they  reach  the 
principal  focus.  The  rays  are  thus  reflected  out  laterally 
through  an  opening  in  the  telescope  tube,  and  are  there 
brought  to  a  focus,  and  the  image  formed  at  the  point 
marked  by  a  heavy  white  line  in  Fig.  25,  instead  of  at 
the  point  inside  the  telescope  marked  by  a  dotted  line. 


)PES. 

t  of  a  rofracting 

nil  the  incident 

there  an  image 

(reflectors)  the 

>r  silvered  glass 

10  figure  showt 

)f  parallel  rays, 

by  reflection  to 

I  focus  may  be 

f  the  refracting 

are  of  the  kinds 
)ye-piece  would 


K  IMAOB. 

oint  F,  and  the 
ith  the  inddeDt 
d  to  remedy  this 
le  fhe  two  most 

ytm  the  rays  of 
bo  fall  on  a  small 
■e  they  reach  the 
ted  out  laterally 
le,  and  are  there 
led  at  the  point 
i5,  instead  of  at 
»y  a  dotted  line. 


RKFLKCTtNO   TSLBBGOPKS. 


07 


This  focal  image  is  then  examined  by  means  of  an  or- 
dinary eye-piece,  the  head  of  the  observer  being  outside 
of  the  telescope  tube. 

Tills  device  is  the  invention  of  Sir  Isaac  Nkwton. 


HBWTONIAN  TBLBSCOPB. 


FiOw  M. 

CAflERnRAINTAN  TKI^BSCOTB. 


Tlie  Oalisegr&iman  Teietiooi>e. — In  this  form  a  second- 
ary convex  mirror  is  piaced  in  the  tube  of  the  telescope 


'-~«.sSB^PIB««WB'"- 


r.8 


AHTHONOMr. 


|i 


abont  three  ■ 'tii«  ,jf  Uie  wiiy  from  the  hirge  HptMtuiutn 
to  the  fociiH.  The  riiyH,  after  l>eing  roHeetetl  from  the 
largo  8))ecuhiin,  fall  oa  this  mirror  befoit)  reaching  the 
focus,  and  are  reHected  back  again  to  the  Bpvculuni ;  an 
opening  is  made  in  the  centre  of  the  latter  to  lot  the  ravs 
imm  through.  The  position  and  curvature  of  the  secondary 
mirror  are  adjusted  so  that  the  focus  shall  be  formed  just 
after  passing  through  the  opening  in  the  speculum. 

In  this  telescope  the  obsurvet  stands  behind  or  under 
the  speculum,  and,  with  the  oyo-pieco,  looks  through  the 
opening  in  the  centre,  in  the  direction  of  the  object. 
This  form  of  reflector  is  much  more  convenient  in  use 
than  the  Newtonian,  in  using  which  the  observer  has  to 
be  near  the  top  of  the  tube. 

This  form  was  devised  by  Cabrkorain  in  1672. 

Tho  advantages  of  reflectors  are  found  in  their  cheap- 
ness, and  in  the  fact  that,  supposing  the  mirrors  perfect  in 
tigure,  all  the  rays  of  the  spectrum  are  brought  to  one 
focus.  Thus  the  reflector  is  suitable  for  spectroscopic  or 
]>hotographic  researches  without  any  change  from  its  or- 
dinary fonn.  This  is  not  true  of  the  refractor,  since  the 
rays  by  which  we  now  photograph  (the  blue  and  violet 
rays)  are,  in  that  instrument,  owing  to  the  secondary 
spectrum,  brought  to  a  focus  slightly  different  from  that 
of  the  yellow  and  adjacent  rays  by  moans  of  which  we 

060* 

Beflectors  have  been  made  as  large  as  six  feet  in  aper- 
ture, the  greatest  being  that  of  Lord  Robse,  but  those 
which  have  been  most  successful  have  hardly  ever  been 
larger  than  two  or  three  feet.  The  smallest  satellite  of 
Satntm  {Minuu)  was  discovered  by  Sir  Wiujam  Hersohel 
with  a  four-foot  speculum,  but  all  the  other  satellites  dis- 
covered by  him  were  seen  with  mirrors  of  about  eighteen 
inches  in  aperture.  With  these  the  vast  majority  of  his 
faint  nebnlsB  were  also  discovered. 

The  satellites  of  Neptune  and  TTrantts  were  discovered 
by  Lassell  with  a  two-foot  speculum,  and  much  of  the 


nKFLKcrmn  TKijjsropfss. 


m 


largo  Rpecuium 
leotud  from  tlio 
m  reaching  the 
J  spvculuin  ;  an 
ir  to  lot  the  rava 
of  the  secondary 
i  Im)  formed  just 
tpeculum. 
behind  or  nndor 
x>k8  through  the 
I  of  tho  object, 
mveniont  in  uro 
)  observer  has  to 

in  1672. 

in  their  chcap- 
nirrors  perfect  in 
brought  to  one 
spectroscopic  or 
mge  from  its  or- 
f ractor,  since  the 
)  blue  and  violet 
o  the  secondary 
ferent  from  that 
lans  of  which  we 

\  six  feet  in  aper- 
RosBE,  but  those 
hardly  ever  been 
allest  satellite  of 
II4.IAM  Hersohel 
ther  satellites  dis- 
at  about  eighteen 
t  majority  of  his 

» were  discovered 
and  much  of  the 


work  of  Lord  Rohhk  has  boon  doiio  with  liitt  throo-foot 
mirror,  iuHtead  of  liiw  (Hilobmtod  nix  foot  oin\ 

From  tho  tinu)  of  Nkwton  till  (luito  rccontly  it  wa« 
usual  to  make  tho  largo  mirror  or  objoj-tivo  out  of  Bpcu- 
Inni  motal,  a  brilliant  alloy  liublo  to  tanuHh.  Whon  tho 
mirror  was  onco  tiirnishod  through  cxjKWuro  to  tho 
woathor,  it  could  bo  ronowod  only  by  a  proccBS  of  jwlish- 
ing  almost  equivalent  to  figuring  and  polishing  tho  mirror 
anew.  Consequontly,  in  such  a  speculum,  after  the  cor- 
rect f  jrtn  and  polish  wore  attained,  there  was  groat  diffi- 
culty in  preserving  them.  In  rocont  years  this  difficulty 
has  been  largely  ovorcomo  in  two  ways  :  first,  by  im- 
provements in  the  composition  of  the  alloy,  by  which  its 
liability  to  tarnish  under  exposure  is  greatly  diminished, 
and,  secondly,  by  a  plan  proposed  by  Foucault,  which 
C(m8ist8  in  making,  onco  for  all,  a  mirror  of  ghws  which 
will  always  retain  its  good  figure,  and  depositing  upon  it  a 
thin  film  of  silver  which  may  be  removed  and  restored 
Mrith  little  labor  as  often  as  it  becomes  tarnished. 

In  this  way,  one  important  defect  in  the  reflector  has 
been  avoided.  Another  great  defect  has  been  less  success- 
fully treated.  It  is  not  a  pntcess  of  exceeding  difficulty 
to  give  to  the  reflecting  surface  of  either  metal  or  glass 
the  correct  parabolic  shape  by  which  the  incident  raya  are 
brought  accurately  to  one  focus.  But  to  maintain  this 
shape  constantly  when  the  mirror  is  mounted  in  a  tube, 
and  when  this  tube  is  directed  in  succession  to  various 
parts  of  the  sky,  is  a  mechanical  problem  of  extreme  diffi- 
culty. However  the  mirror  may  be  supported,  all  the 
unsupported  points  tend  by  their  weight  to  sag  away  from 
the  proper  position.  "Wben  the  mirror  is  pointed  near 
the  horizon,  this  effect  of  flexure  is  quite  different  from 
what  it  is  when  pointed  near  the  zenith. 

As  long  as  the  mirror  is  small  (not  greater  than  eight  to 
twelve  inches  in  diameter),  it  is  foimd  easy  to  support  it 
so  that  these  variations  in  the  strains  of  flexure  have  little 
practical  effect.     As  we  increase  its  diameter  up  to  48  or 


mmm 


10 


AaTRONOMT. 


72  inches,  the  effect  of  flexure  rapidly  increases,  and 
special  devices  have  to  he  used  to  couuterhalaiice  the 
injury  done  to  the  shape  of  the  mirror. 

§  3.    CHBONOMETEBS  AND  CLOCKS. 

In  Chapter  I.,  §  5,  wo  described  how  the  right  ascen. 
sions  of  the  heavenly  bodies  are  measured  by  the  times 
of  their  transits  over  the  meridian,  this  quantity  increas- 
ing by  a  minute  of  arc  in  four  seconds  of  time.  In  order 
to  determine  it  with  all  required  accuracy,  it  is  necessary 
that  the  time-pieces  with  wliich  it  is  measured  shall  go 
with  the  greatest  possible  precision.  There  is  no  great 
difficulty  in  making  astronomical  measures  to  a  second 
of  arc,  and  a  star,  by  its  diurnal  motion,  passes  over  this 
space  in  one  fifteenth  of  a  second  of  time.  It  is  there- 
fore desirable  that  the  astronomical  clock  shall  not  vary 
from  a  uniform  rate  more  than  a  few  hundredths  of  a 
second  in  the  course  of  a  day.  It  is  not,  however, 
necessary  that  it  should  be  perfectly  correct ;  it  may  go 
too  fast  or  too  slow  without  detracting  from  its  char- 
acter for  accuracy,  if  the  intervals  of  time  which  it 
tellfl  off—hours,  minutes,  or  seconds— are  always  of  ex- 
actly the  same  length,  or,  iu  other  words,  if  it  gains  or 
loses  exactly  the  same  amount  every  hour  and  every  day. 

The  time-piecos  used  in  astronomical  observation  are 
the  chronometer  and  the  clock. 

The  chronmnMer  is  merely  a  very  perfect  time-piece 
with  a  balance-wheel  so  constructed  that  changes  of  tem- 
perature have  the  least  possible  effect  upon  the  time  of  its 
oscillation.  Such  a  balance  is  called  a  eom^pematum  bal- 
ance. 

The  ordinary  house  clock  goes  faster  in  cold  than  in 
warm  weather,  because  the  pendulum  rod  shortens  under 
the  influence  of  cold.  This  effect  is  such  that  the  clocl 
will  gain  about  one  second  a  day  for  every  fall  of  3°  Cent. 
{ft" A  Fahr.)  in  the  temperature,  supposing  the  pendulum 


THE  ASTRONOMICAL  CLOCK. 


11 


increases,   and 
iterbalanco   the 


[jOCKB. 

:ho  right  ascen. 
d  by  the  times 
uantity  increas- 
time.  In  order 
•,  it  is  necessary 
lasured  shall  go 
ere  is  no  great 
■£S  to  a  second 
passes  over  this 
e.  It  is  there- 
c  shall  not  vary 
lundredths  of  a 
not,  however, 
rect ;  it  may  go 
from  its  char- 
time  which  it 
3  always  of  ex- 
3,  if  it  gains  or 
and  every  day. 
observation  are 

rfect  time-piece 
changes  of  tem- 
1  the  time  of  its 
vr^^ensaMon  bal- 

in  cold  than  in 
i  shortens  under 
li  that  the  clocE 
rfaUof  3°0ent. 
g  the  pendulnm 


rod  to  be  of  iron.  Such  changes  of  rate  would  be  entirely 
inadmissible  in  a  clock  used  for  iistronomical  purposes. 
The  astronomical  'Jock  is  therefore  provided  with  a  com- 
pensation pendulum,  by  which  the  disturbing  effects  of 
changes  of  temperature  are  avoided. 

There  are  two  forms  now  in  use,  the  Harrison  (grid- 
iron) and  the  mercurial.  In  the  gridiron  pendulum  the 
rod  is  composed  in  part  of  a  number 
of  parallel  bars  of  steel  and  brass, 
so  connected  together  that  while  the 
expansion  of  the  steel  bars  produced 
by  an  increase  of  temperature  tends 
to  depress  the  hob  of  the  pendulum, 
the  greater  expansion  of  the  brass  bars 
tends  to  raise  it.  When  the  total 
lengths  of  the  steel  and  brass  bars 
have  been  properly  Jidjusted  a  nearly 
perfect  compensation  occurs,  and  the 
centre  of  oscillation  remains,  at  a  con- 
stant distance  from  the  point  of  sus- 
pension. The  rate  of  the  clock,  so 
far  as  it  depends  on  the  length  of  the 
pendulum,  will  therefore  be  constant. 

In  the  mercniial  pendulum  the 
weight  which  f  onus  the  bob  is  a 
cylindric  glass  vessel  nearly  filled 
with  mercury.  With  an  increase  of  temperature  the  steel 
suspension  rod  lengthens,  thus  throwing  the  centre  of 
osdllation  away  from  the  point  of  suspension ;  at  the 
same  time  the  expanding  mercury  rises  in  the  cylinder, 
and  tends  therefore  to  raise  the  centre  of  oscillation. 
When  the  lengdi  of  the  rod  and  the  dimensions  of  the 
cylinder  of  mercury  are  properly  proportioned,  the  centre 
of  osdllation  is  kept  at  a  constant  distance  from  the  point 
of  suspension.  Other  methods  of  making  tiiis  compensa- 
tion have  been  used,  but  these  are  the  two  in  most  gen- 
eral use  for  astronomical  clot-.ks. 


Pig.  27.— oRroiRON 


■vmmmmmmmmimiitmiiM 


Hi 


78 


ABTBONOMT. 


Ill 


The  Mtreetion  of  a  chronometer  (or  clock)  is  the  quantity  of  time 
(expressed  in  hours,  minutes,  seconds,  and  decimals  of  a  second) 
which  it  is  necessary  to  add  algebraically  to  the  indication  of  the 
hands,  in  order  that  the  sum  may  be  the  correct  time.  Thus,  if  at 
sidereal  0\  May  18,  at  New  York,  a  sidereal  clock  or  chronometer 
indicates  23''  58"'  20* -7,  itc  correction  is  +  1»'  89'. 8 ;  if  af.O''  (siderwl 
noon),  of  May  17,  its  correction  was  +  1"'  88- -8,  its  daily  rate  or  the 
change  of  its  correction  in  a  sidereal  day  is  +  1*0:  in  other  words, 
this  clock  is  loring  1"  daily. 


For  clock  Blow  the  sign  of  the  eorreetion  is  + ; 
«'  ''  fast  "  "  "  "  "  '8  — ; 
"      "  gaining "     "    "    "       rate 


loting 


18  —  5 

is  +  . 


A  clock  or  chronometer  may  be  well  compensated  for  temperature, 
and  yet  its  rate  may  be  gaining  or  losing  on  the  time  it  is  intended 
to  keep :  it  is  not  even  necessary  that  the  rate  should  be  small  (ex- 
cept that  a  small  rate  is  practically  convenient),  provided  only  that 
it  IS  constant.  It  is  continually  necessary  to  compute  the  clock  cor- 
rection at  a  given  tims  from  its  known  correction  at  some  other  time, 
and  its  known  rate.  If  for  some  definite  instant  we  denote  the  time 
as  shown  by  the  clock  (technically  "the  clock-face")  by  2',  the  true 
time  by  T  and  the  clock  correction  by  a  T,  we  have 

T  =  T  +  A  r,  and 

i,T  =  r  -  T. 

In  alt  obserratories  and  at  sea  observations  are  made  daily  to  de- 
termine A  T.  At  the  instant  of  the  observation  the  time  T  is  noted 
by  the  clock;  from  the  data  of  the  observation  the  time  r  is  com- 
puted. If  these  agree,  the  clock  is  correct.  If  they  differ,  ATia 
found  from  the  above  equations. 

If  by  observation  we  have  found 

A  7»  =  the  clock  correction  at  a  clock-time  7», 
A  7*  =  the  clock  correction  at  a  clock-time  T, 
ST  =:  the  clock  rate  in  a  unit  of  time, 


we  have 


Ar=  AT, +  d2'(5P-7',) 


where  T  —  T,  must  be  expressed  in  days,  hours,  etc.,  according  as 
dr  is  the  rate  in  one  day,  one  hour,  etc.  :,,.-,.        . 

When,  therefore,  the  clock  correction  A  T.  and  rate  ST  have  been 
determined  for  a  certain  instont,  T.,  we  can  deduce  the  true  time 
from  the  clock-face  2*  at  any  other  Instant  by  the  equation  r  =  T 
.  AT*  +  dr(7'—  !•)•  "  ^^  dock  correction  has  been  deter- 
mined at  two  different  ttmes,  T.  and  T  to  be  A  T.  and  A  T,  the  rate 
is  inferred  from  the  equation 


6T. 


AT-  Ag> 


the  quantity  of  time 
nmals  of  a  second) 
:he  indication  of  the 
t  time.  Thus,  if  at 
Dck  or  chronometer 
'•8;  if  aiO'' (sidereal 
,  its  daily  rate  or  the 
*-0:  in  other  words, 


■ion  is  + ; 

is  —  ; 

I       is  — ; 

is  +  . 

ited  for  temperature, 
le  time  it  is  intended 
should  be  small  (ex- 
),  provided  only  that 
»mpute  the  clock  cor- 
n  at  some  other  time, 
it  we  denote  the  time 
ace")  by  2\  the  true 
have 


are  made  daily  to  de- 
>n  the  time  T  is  noted 
a  ths  time  T  is  com- 
If  they  differ,  LTxs 


;k-time  T», 
ck-time  7, 
me, 

ITS,  etc.,  according  as 

md  rate  ^  7  have  been 
deduce  the  true  time 
the  equation  7*  =  7 
ction  has  been  deter- 
,  T»  and  A  T,  the  rate 


THE  ASTRONOMICAL  CLOCK, 


73 


These  equations  apply  only  so  long  as  we  can  regard  the  rate  as 
comtnnt.  As  observations  can  bo  made  only  in  clear  weather,  it  is 
plain  that  during  periods  of  overcast  sky  wc  must  depend  on  these 
equations  for  our  knowledge  of  7" — i.e.,  the  true  time  at  a  clock- 
time  T. 

The  intervals  between  the  determination  of  the  clock  correction 
should  be  small,  since  even  with  the  best  clocks  and  chronometers 
too  much  dependence  must  not  be  placed  upon  the  rate.  The  follow- 
ing example  from  Cbauvemet's  Astronomy  will  illustrate  the  practi- 
cal processes : 

"  Example. — At  sidereal  noon,  May  5,  the  correction  of  a  sidereal 
clock  is— 16"'  47'0;  at  sidereal  noon,  May  12,  it  is  —  16'"  IS'-SO; 
what  is  the  sidereal  time  on  May  25,  when  the  clock-face  is  11"  13'" 
12" -6,  supposing  the  rate  to  be  uniform  ? 

May  5,  correction  =  —  IB""  47'. 30 
"  12,         "  =  -16"' 13'.  50 

7  days'  rate    =r+         83' "50 
dT=  +  4'.829. 

Taking  then  as  our  starting-point  T^  =  May  12,  O**,  we  have  for  the 
interval  to  T=  May  25,  ll"-  13'«  12'-6,  T-  To  =  W^  W  13'"  12"e 
=  18''-467.     Hence  we  have 

Ar.,=  -    16»l'}«-60 
dT(T—  To)=  +      1"    fi'OS 


AT=    -    15"    8'-47 

T=n*'  18'»J2;^^60 

7»=  10^  SS"    4'.  13 

But  in  this  example  the  rate  is  obtained  for  one  true  sidereal  day, 
while  the  unit  of  the  interval  18''-467  is  a  sidereal  day  as  shovn  by 
the  clock.  The  proper  interval  with  which  to  compute  the  n\te  in 
this  case  is  W  10^  68"  4*  18=  18'' -457,  with  which  we  find 

AT»=  —   Id"  IS'. 50 

6Ty  18-457=  +      1-    4'98 

A  7*  =  —    IS"    8'. 52 

T  =  11''  18"' 12' -60 

7*- 10'' 68"    4*  08 

This  repetition  wVl  'ot  rendered  unnece^^sary  by  always  giving  the  rcte 
in  a  vntt  of  the  ek>A.  Thus,  suppose  that  on  June  8,  at  4"  11*"  12'-86 
by  the  clock,  we  have  found  the  correctiori  +  2*"  10*  14;  and  on 
June  4,  at  W  ^7*"  49*. 89  we  L.*  .^  fo>jnd  tba  correction  -i-  2"'  10<-89 ; 
the  rate  in  cm  iuiw  of  the  eloek  will  be 


iiT  = 


-^9••7S 


84'11'M 


rr  =   t-  0'-2868." 


■■M 


.U:,  -^ 


74  ASTRONOMY. 

I  4.    THE  TRANSIT   INSTBUMENT. 

The  meridian  transit  instrument,  or  briefly  the  "  tran- 
sit," is  used  to  observe  the  transits  of  the  heavenly  bodieg. 


Fig.  28.— a  tiukbit  ihstbiimbnt. 

and  from  the  times  of  these  transits  as  read  from  the 
clock  to  determine  either  the  corrections  of  the  clock  or 
the  right  ascension  of  the  observed  body,  as  explained  in 
Chapter  I.,  §5. 


[TMENT. 

briefly  the  "  traii- 
3  heavenly  bodies. 


BNT. 


18  read  from  the 
nB  of  the  clock  or 
y,  as  explained  in 


THE  TnANSIT  INaTRUMENT.  tS 

It  has  two  general  forms,  one  (Fig.  28)  for  use  in  fixed 
observatories  and  one  (Fig.  29)  for  nse  in  the  fiekl 

It  consists  essentially  of  a  telescope  TT  TFiir  28^ 
mounted  on  an  axis  F  Fat  right  angle's  to  it      ^    ^'       ^ 


Pig.  29.-P011TABLE  transit  mSTRlWKNT. 

The  ends  of  this  axis  terrainate  in  accurately  cvlindrio^l 
Bteel  pivots  which  re«t  in  metallic  bearing  FfTI.^ 
like  the  letter  Y,  and  hence  called  the  f,  '         *^ 


iWi^aBBitjwiiffiwMaw'' 


re 


AaTltONOMT. 


These  are  fastened  to  two  pillars  of  stone,  l)rick,  or 
iron.  Two  counterpoises  W  W  are  connected  with  the 
axis  as  in  the  plutc,  so  as  to  take  a  largo  portion  of  the 
weight  of  the  axis  and  telescope  from  the  Ys,  and  thus  to 
diniinish  the  friction  npon  these  and  to  render  the  rota- 
tion about  V  V  more  eaay  and  regular.  In  the  ordinary 
use  of  the  transit,  the  line  F  F  is  placed  accurately  level 
and  perpendicular  to  the  meridian,  or  in  the  east  and  west 
line.  To  effect  this  *'  adjustment,"  there  are  two  sets  of 
adjusting  screws,  by  which  the  ends  of  F  F  in  the  Ys  may 
be  moved  either  up  and  down  or  north  and  south.  The 
plate  gives  the  form  of  transit  used  in  permanent  observa- 
tories, and  shows  the  observing  chair  G^  the  reversing  car- 
riage R,  and  the  level  L.  Tl  arms  of  the  latter  have 
Y'b,  which  can  be  placed  over  the  pivots  F  F. 

The  line  of  coUiination  of  the  transit  telescope  is  the 
line  drawn  through  the  centre  of  the  objective  perpendic- 
ular to  the  rotation  axis  V  V. 

The  reticle  is  a  network  of  fine  spider  lines  placed  in 
the  focus  of  the  objective. 

In  Fig.  30  the  circle  represents  the  field  of  view  of  a 
transit  as  seen  through  the  eye-piece.  The  seven  ver- 
tical Unes,  I,  II,  III,  IV,  V,  VI, 
VII,  are  seven  fine  spider  lines 
tightly  stretched  acroes  a  metal  plate 
or  diaphragm,  and  so  adjusted  as  to 
be  perpendicular  to  the  direction  of 
a  star's  apparent  diurnal  motion. 
This  metal  plate  can  be  moved  right 
and  left  by  five  screws.  Tb'  hori- 
zontal wires,  guide-wires,  a  and  h, 
mark  the  centre  of  the  field.  The 
field  iii  Illuminated  at  night  by  a  lamp  at  the  end  of  the 
axis  which  shinep  through  the  hollow  interior  of  the  lat- 
ter, and  causes  the  field  to  appear  bright.  The  wires  are 
dark  against  a  bright  ground.  The  line  of  sight  is  a  line 
joining  the  centre  of  the  objective  and  the  central  one,  IV, 
of  the  seven  vertical  wires. 


&^ 


TUH  TRANSIT  INSTUUMKNT. 


77 


me,   brick,   or 
ictcd  with  tlio 
)ortiou  of  the 
8,  and  thus  to 
inder  the  rota- 
;n  the  ordinary 
iccurately  level 
e  east  and  west 
are  two  sets  of 
In  the  Ys  may 
id  south.    The 
lanent  observa- 
s  reversing  car- 
the  latter  have 
VV. 

elescope  is  the 
jtive  perpendic- 

lines  placed  in 

Id  of  view  of  a 
The  seven  ver- 

II,  IV,  V,  yi, 

no   spider    lines 
08B  a  metal  plate 
10  adjusted  as  to 
the  direction  of 
diurnal   motion. 
1  be  moved  right 
«wfc.     Tb'  hori- 
i-vn/reB,  a  and  b, 
the  field.     The 
,  the  end  of  the 
iterior  of  the  lat- 
.     The  wires  are 
of  »ight  is  a  line 
B  central  one,  IV, 


The  whole  transit  is  in  adjustment  when,  first,  the  axis 
V  V  is  horizontal ;  second,  when  it  lies  east  and  west ; 
and  third,  when  the  line  of  sight  and  the  line  of  collinia- 
tion  coincide.  When  these  conditions  are  fulfilled  the 
line  of  sight  intersects  the  celestial  sphere  in  the  meridian 
of  the  place,  and  when  T  T\9,  rotated  about  V  V  the  line 
of  sight  marks  out  the  meridian  on  the  sphere. 

In  practico  the  three  adjustments  are  not  exactly  made,  since  it  is 
impossible  to  effect  them  with  mathematical  precision.  The  errors 
of  each  of  them  are  first  made  as  small  as  is  convenient,  and  are  then 
determined  and  allowed  for. 

To  find  the  error  of  level,  we  place  on  the  pivots  a  fine  level  (shown 
in  position  in  the  figure  of  the  portable  transit),  and  determine  how 
much  higher  one  pivot  is  than  the  other  in  terms  of  the  divisions 
marked  on  the  level  tube.  Such  a  level  is  shown  in  Fig.  4  of  plate 
85,  page  86.  The  value  of  one  of  these  divisions  in  seconds  of  arc 
can  be  determined  by  knowing  the  length  I  of  the  whole  level  and 
the  number  n  of  divisions  through  which  the  bubble  will  run  when 
one  end  is  raised  one  hundredth  of  an  inch. 

If  I  is  the  length  of  the  level  in  inches  or  the  radius  of  the  circle 
in  which  either  end  of  the  level  moves  when  it  is  raised,  then  as 
the  radius  of  any  circle  is  equal  to  57°  •  296,  3437'  •  75  or  206,264"  •  8, 
we  have  in  thui  particular  circle  one  inch  =  206, 264" -8  -s-  I; 
0-01  inch  =  2(0^264 -8  -4-  100  Z  =  a  certain  arc  in  seconds,  say  a". 
That  is,  n  divisions  =  a",  or  one  division  d  =  a"  -i-  n. 

The  error  of  eoUimation  can  be  found  by  pointing  the  telescope 
at  a  distant  mark  whose  image  is  brought  to  the  middle  wire.  The 
telescope  (with  the  axis)  is  then  lifted  bodily  from  the  Ys  and  re- 
placed so  that  the  axis  V  Fis  reversed  end  for  end.  The  telescope  is 
again  pointed  to  the  distant  mark.  If  this  is  still  on  the  middle 
thread  the  line  of  sight  and  the  line  of  eoUimation  coincide.  If  not, 
the  reticle  must  be  moved  bodily  west  or  east  until  these  conditions 
are  fultiUed  after  repeated  reversals. 

To  find  the  error  of  mimuth  or  the  departure  of  the  direction  of 
VV  from  an  east  and  west  line,  we  must  observe  the  transits  of 
two  btars  of  different  declinations  d  and  <S,  and  right  ascensions  a 
and  a'.  Suppose  the  clock  to  be  running  correctly — that  is,  with  no 
rate — and  tne  sidereal  times  of  transit  of  the  two  stars  over  the  mid> 
die  thread  to  be  0  and  0'.  If  0  —  6'  =  «  —  «',  »hea  the  mid4lc  wii» 
is  in  the  meridian  and  the  azimuth  is  zero.  For  if  the  nziinvitli 
was  not  zero,  but  the  west  end  of  the  axis  w«us  tou  far  south,  for 
example,  the  line  of  sight  would  fall  eant  <«l  the  meridian  for  a 
south  stifkr,  and  further  and  further  cast  tK  ftirthcH  !«>wth  the  star 
was.  Hence  if  the  two  stars  have  widel>  tliff(ro»t  detlinationa  6 
and  <5',  then  the  star  furthest  south  would  lom*  ]>ioportion»toly 
sooner  to  the  middle  wire  than  the  otlK''t  :««Ki  U  —  0'  wowkl  be 
different  from  a  —  u'.     The   amount  of   irM»  diSereBC«   give!>   a 


mm 


MMMMI 


78 


A8TR0N0MT. 


means  of  deducing  tho  deviation  oi  A  A  from  an  east  and  west 
tine.  In  a  similar  way  the  effect  of  a  given  error  of  level  on  the 
time  of  the  transit  of  a  star  of  declination  6  is  found. 

Methods  of  Obaerving  with  the  Transit  Instrument.— 
We  ]i.)ve  »o  far  asHUiiicd  tliat  the  time  of  a  star's  transit 
over  the  middle  tliread  was  known,  or  could  be  noted. 
It  is  neccHsary  to  speak  more  in  detail  of  how  it  is  noted. 
When  tho  telescope  is  pointed  to  any  star  the  earth's 
diurnal  motion  will  carry  the  image  of  the  star  slowly 
across  the  field  of  view  of  the  telescope  (which  is  kept 
fixed),  as  before  explained.  As  it  crosses  each  of  the 
threads,  the  time  at  which  it  is  exactly  on  the  thread  is 
noted  from  the  clock,  which  must  be  near  the  transit. 

The  mean  of  these  times  gives  the  time  at  which  this 
star  was  on  the  middle  thread,  the  threads  being  at  equal 
intervals  ;  or  on  the  "  mean  thread,"  if,  as  is  the  case  in 
practice,  they  are  at  unequal  intervals. 

if  it  were  possible  for  an  astronomer  to  note  the  exact 
instant  of  the  transit  of  a  star  over  a  thread,  it  is  plain 
that  one  thread  would  be  sufficient ;  but,  as  all  estima- 
tions of  this  time  are,  from  the  very  natifre  of  the  case, 
but  approximations,  several  threads  are  inserted  in  order 
that  the  accidental  errors  of  estimations  may  be  eliminated 
as  far  as  possible.  Five,  or  at  most  seven,  threads  are 
sufficient  for  this  purpose.  In  the 
figure  of  the  reticle  of  a  transit  instru- 
ment the  star  (the  plimet  Vemta  in  this 
ciise)  may  enter  on  the  right  hand  in  the 
figure,  and  may  be  supposed  to  cross 
each  of  the  wires,  the  time  of  its  tran- 
sit over  each  of  them,  or  over  a  suffi- 
cient number,  being  noted.  The 
method  of  noting  this  time  may  be  best 
understood  by  referring  to  the  next  figure.  Suppose  that 
the  line  in  the  middle  of  Fig.  32  is  one  of  the  transit- 
threads,  and  that  the  star  is  passing  from  the  right  hand 
of  the  figure  toward  the  left ;  if  it  in  on  this  wire  at  an 


Pio.  81. 


THE  TRANSIT  HfSTRVMENT. 


79 


%n  east  and  west 
)r  of  level  on  the 
d. 

Instrument.— 
a  star's  transit 
>uld  be  noted, 
ow  it  is  noted, 
tar  the  earth's 
le  star  slowly 
which  is  kept 
38  each  of  the 

the  thread  is 
the  transit. 

at  which  this 

being  at  equal 

18  is  the  case  in 

note  the  ^Must 
■ead,  it  is  plain 
r,  as  all  estima- 
te of  the  case, 
iserted  in  order 
\y  be  eliminated 
en,  threads  are 
rpose.  In  the 
a  transit  instra- 
et  Ventw  in  this 
■ight  hand  in  the 
pposed  to  cross 
time  of  its  tran- 
or  over  a  suffi- 
noted.  The 
ime  may  be  best 
.  Suppose  that 
of  the  transit- 
the  right  hand 
this  wire  at  an 


Fie.  82. 


exact  second  by  the  clock  (which  is  always  near  the  ob- 
server, beating  seconds  audibly),  this  second  must  be  writ- 
ten down  as  the  time  of  the  transit  over  this  thread.  As 
a  rule,  however,  the  transit  cannot  occur  on  the  exact 
beat  of  the  clock,  but  at  the  seventeenth  second  (for  exam- 
ple) the  star  may  be  on  the  right  of  the  wire,  say  at  a  ; 
while  at  the  eighteenth  second 
it  will  have  passed  this  wire  and 
may  be  at  h.  If  the  distance  of 
a  from  the  wire  is  six  tenths  of 
the  distance  a  5,  then  the  time 
of  transit  is  to  be  recorded  as  — 
hours  —  minutes  (to  be  taken 
from  the  clock-face),  and  seven- 
teen and  ^x  tenths  seconds ;  and  in  this  way  the  transit 
over  each  wire  is  observed.  This  is  the  method  of  "  eye- 
and-ear"  observation,  the  basis  of  such  work  as  we  have 
described,  and  it  is  so  called  from  the  part  which  both  the 
eye  and  the  ear  play  in  the  appreciation  of  intervals  of  time. 
The  ear  catches  the  beat  of  the  clock,  the  eye  fixes  the  place 
of  the  sti  r  at  <z  ;  at  the  next  beat  of  the  clock,  the  eye  fixes 
the  star  at  ft,  and  subdivides  the  space  a  b  into  tenths,  at 
the  same  time  appreciating  the  ratio  which  the  distance 
from  the  thread  to  a  bears  to  the  distance  a  h.  This  is 
recorded  as  above.  This  method,  which  is  still  used  in 
many  observatories,  was  introduced  by  the  celebrated 
Bbadlet,  astronomer  royal  of  England  in  1750,  and  per- 
fected by  Maskeltme,  his  successor.  A  practiced  observer 
can  note  the  time  within  a  tenth  of  a  second  in  three  cases 
out  of  four. 

There  is  yet  another  method  now  in  common  use, 
which  it  is  necessary  to  understand.  This  is  called  the 
American  or  chronographic  method,  and  consists,  in  the 
present  practice,  in  the  use  of  a  sheet  of  a  paper  wound 
about  and  fastened  to  a  horizontal  cylindrical  barrel, 
which  is  caused  to  revolve  by  machinery  once  in  one  min- 
ute of  time.     A  pen  of  glass  which  will  make  a  continu- 


^*mmtm 


riitiWiiiiirntwimiWT'iiillMlili •  Ifirti  I  n   imii 


tttmlm 


,U.ni 


ao 


AHTliONOMr. 


ouB  lino  is  allowed  to  rest  on  the  pajxir,  and  to  this  jien  a 
continuous  motion  of  translation  in  the  direction  of  the 
length  of  the  cylinder  is  given.  Now,  if  the  pen  is  allow- 
ed to  mark,  it  is  evident  that  it  will  trace  on  the  paper  an 
endless  spiral  line.  An  electric  current  is  caused  to  run 
through  tlio  ("iV/serving  clock,  through  a  key  which  is  held 
in  the  observer's  hand  and  through  an  electro-magnet 
connected  with  the  pen. 

A  simple  device  enables  the  clock  every  second  to  give 
a  slight  lateral  motion  to  the  pen,  which  lasts  about  a 
thirtieth  ol  a  second.  Thus  every  second  is  automatically 
marked  by  the  clock  on  the  chronograph  paper.  The  ob- 
server also  has  the  power  to  make  a  signal  by  his  key 
(easily  distinguished  from  the  clock-signal  by  its  different 
length),  which  is  likewise  permanently  registered  on  the 
sheet.  In  this  way,  after  the  chronograph  is  in  motion, 
the  observer  has  merely  to  notice  the  instant  at  which  the 
star  is  <m  the  thread,  and  to  press  the  key  at  that  moment. 
At  any  subsequent  time,  he  must  mark  some  hour,  min- 
ute, and  second,  taken  from  the  clock,  on  the  sheet  at  its 
appropriate  place,  and  the  translation  of  the  spaces  on 
the  sheet  into  times  may  be  done  at  leisure. 


%  6.    OaADXTATED  OIBOItBS. 

Koarly  every  datum  in  practical  astronomy  depends 
either  directly  or  indirectly  upon  the  measure  of  an  angle. 
To  make  the  necessary  measures,  it  is  customary  to  em- 
ploy what  are  called  graduated  or  divided  circles.  These 
are  made  of  metal,  as  light  and  yet  as  rigid  as  possible, 
and  they  have  at  their  circumferences  a  narrow  flat  band 
of  silver,  gold,  or  platinum  on  which  fine  radial  lines 
called  "  divisions"  are  cut  by  a  "  dividing  engine"  at 
regular  and  equal  intervals.  These  intervals  may  be 
of  10',  5',  or  2',  according  to  the  size  of  the  circle 
and  the  degree  of  accuracy  desired.  The  narrow  band 
is  called  the  divided  limb,  and  the  circle  is  said  to  be  di- 


•'Hr 


riiK  vhmNfhm. 


81 


d  to  thi8  jien  a 
irection  of  the 
le  pen  is  allow- 
in  the  paper  an 
caused  to  mn 
y  whicli  is  held 
electro-magnet 

second  to  give 

lasts  about  a 
is  automatically 
aper.  The  ob- 
nal  by  his  key 

by  its  different 
;istered  on  the 
h.  is  in  motion, 
nt  at  which  the 
at  that  moment. 
>me  hour,  min- 
the  sheet  at  its 

the  spaces  on 


momy  depends 
ure  of  an  angle, 
istomary  to  em- 
circles..  These 
^d  as  possible, 
arrow  flat  band 
ine  radial  lines 
ling  engine"  at 
terTftIs  may  be 
5  of  the  circle 
le  narrow  band 
>  said  to  be  di- 


Fio.  88. 


vided  to  10',  r»',  y'.  The  separate  diviBJons  are  numbered 
consecutively  from  0"  to  30(>^  or  from  0"  to  1)0°,  etc.  The 
graduated  circle  has  an  axiH  at  itH  centre,  and  to  this  may 
be  attached  the  telescope  by  whicli  to  view  tlie  pointti 
whose  angiilar  distance  is  to  be  dcteriuiued. 

To  this  centre  is  also  attached  an  arm  wliicli  revolves 
with  it,  and  by  its  motion  past  a  certain  nuinbur  of  divi- 
sions on  the  circle,  determines  the  angle  through  which  the 
centre  has  been  rotated.  This  arm  is  called  the  index 
arm,  and  it  usually  carries  a  vernier  on  its  extremity, 
by  means  of  which  the  spaces  on 
the  graduated  circle  are  subdivided. 
The  reaijimj  of  the  circle  when  the 
index  a  '  in  any  position  is  the 

number  'agrees,    minutes,    and 

seconds  w  cH  correspond  to  that  po- 
sition ;  when  the  index  arm  is  in  an- 
other position  there  is  a  different 
reading,  and  the  differences  of  the  two 
readings  S' — <S",  S* — S*,  S*—S*  are  the  angles  through 
which  the  index  arm  has  turned. 

The  process  of  measuring  the  angle  between  the  objects 
by  means  of  a  divided  circle  consists  then  of  pointing  the 
telescope  at  the  first  object  and  reading  the  position  of  the 
index  arm,  and  then  turning  the  telescope  (the  index 
arm  turning  with  it)  until  it  points  at  the  second  object, 
and  again  reading  tlie  position  of  the  index  arm.  The 
difference  of  these  readings  is  the  angle  sought. 

To  facilitate  the  determination  of  the  exact  reading  of 
the  circle,  we  have  to  employ  special  devices,  as  the 
vernier  and  the  reading  microscope. 

The  Vernier.— In  Fig.  34,  M  JV  ia  a  portion  of  the 
divided  limb  of  a  graduated  circle ;  Ci)  is  the  index  arm 
which  revolves  with  the  telescope  about  the  centre  of  the 
circle.  The  end  ah  of  CD  k  also  a  part  of  a  circle  con- 
centric with  Mlf^,  and  it  is  divided  into  n  parts  or  divi- 
sions.     The  length  of  these  n  parts  is  so  chosen  that  it  is 


mumm 


1 


i, ' 


82 


AHTRONOMY. 


tltc  BUiiio  UH  thut  of  {a — 1)  purta  on  tliu  divided  limb  M  N 
or  tho  roversc. 

The  first  stroke  a  is  tlio  zero  of  tho  vernier,  and  the 
reading  is  always  determined  by  tl»o  position  of  this  zero 
or  pointer.  If  this  hiwa  revolved  past  exactly  twenty  di- 
visions of  tho  eircle,  then  the  angle  to  be  measured  is 
20  X  d,  d  being  tho  value  of  one  division  on  the  limb 
(iV  M)  in  arc. 


FlO.  84.— THR  VKRNIKR. 


Gall  the  angular  value  of  one  division  on  the  vernier  d'\ 

n  —  \  1 

(n  —  l)d  =  n-d', or  d'  = d,BLndd—d'=-df 

d  —  d'  is  called  the  least  count  of  the  vernier  which  is  one 
n*"*  part  of  a  circle  division. 

If  the  zero  a  does  not  fall  exactly  on  a  division  on  the 
circle,  but  is  at  some  other  point  (as  in  the  figtire),  for  ex- 
ample between  two  divisions  whose  numbers  are  P  and 
{P  +  1),  the  whole  reading  of  the  circle  in  this  position  is 
P  X  d+  the  fraction  of  a  division  from  P  to  a. 

If  the  m""  division  of  the  vernier  is  in  the  prolongation 
of  a  division  on  the  limb,  then  this  fraction  Pa  k  m 


I 


ridiid  limb  J/  JV 

vernier,  and  the 
tiun  of  this  zero 
ictiy  twenty  di- 
bu  ineaAiired  is 
on  on  the  limb 


n  the  vernier  d'\ 

dd-d'=-d; 
n    ' 

lier  which  is  one 

,  division  on  the 

e  figtire),  for  ex- 

bers  are  P  and 

n  this  position  is 

Ptoa. 

the  prolongation 

EMStion  Pa  h  m 


msm 


mmm 


..^... 


IMAGE  EVALUATION 
TEST  TARGET  (MT-3) 


/. 


^ 


i 


/J 


i/.. 


1.0 


1.1 


11.25 


Ui|2£   121 

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lu  Ui2   12.2 
■u  |.,A    iiii 

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PhotDgraphic 

Sciences 

Corporation 


li' 


23  WIST  MAIN  STRUT 

WIUTIR.K.Y.  14510 

(716)  •72-4503 


CIHM/ICMH 

Microfiche 

Series. 


CIHIVI/ICIVIH 
Collection  de 
microfiches. 


Canadian  institute  for  Historicai  iVIicroreproductions  /  institut  Canadian  de  microreproductions  historiques 


TUE  MERIDIAN  CIRCLE. 


83 


(d  -  d')  =--d.     In  the  figure  n  =  10,  and  as  the  4th 

division  is  almost  exactly  in  coincidence,  m  =  4,  so  that 

the  whole  reading  of  the  circle  isPxd  +  j^'d.    Ifdia 

10',  for  example,  and  if  the  division  P  is  numbered  297° 
40',  then  this  reading  would  be  297°  44',  the  least  count 
being  1',  and  so  in  other  cases.  If  the  zero  had  started  from 
the  reading  280°  20',  it  must  have  moved  past  17*  24', 
and  this  is  the  angle  which  has  been  measured. 


§  6.    THE  MERIDIAN  CIBCLE. 

The  meridian  circle  is  a  combination  of  the  transit  in- 
strument with  a  graduated  circle  fastened  to  its  axis  and 
moving  with  it.  The  meridian  circle  made  by  Repsold 
for  the  United  States  Naval  Academy  at  Annapolis  is 
shown  in  the  figure.  It  has  two  circles,  c  c  and  c'  c',  finely 
divided  on  their  sides.  The  graduation  of  each  circle  is 
viewed  by  four  microscopes,  two  of  which,  H  B,  are 
shown  in  the  cut.  The  microscopes  are  90°  apart.  The 
cut  shows  also  the  hanging  level  L  Z,  by  which  the 
error  of  level  of  the  axis  AAia  found. 

The  instrument  can  be  used  as  a  transit  to  determine 
right  ascensions,  as  before  described.  It  can  be  also  used 
to  measure  declinations  in  the  following  way.  If  the  tele- 
scope is  pointed  to  the  nadir,  a  certain  division  of  the  cir- 
cles, as  If,  is  under  the  first  microscope.  If  it  is  pointed 
to  the  pole,  the  reading  will  change  by  the  angular  distance 
between  the  nadir  and  the  pole,  or  by  90°  +  ^,  ^  being 
the  latitude  of  the  place  (supposed  to  be  known).  'The 
polar  reading  P  is  thus  known  when  the  nadir  reading 
If  is  found.  If  the  telescope  is  then  pointed  to  various 
stars  of  unknown  polar  distances,  p',  p'\p"',  etc.,  as  they 
successively  cross  the  meridian,  and  if  the  circle  readings 
for  these  stars  are  P',  P",  P"',  etc.,  it  follows  that 
p'  =  P'-P  ;  p"  =  P'-P;  p'"  =  P"'  -  P,  etc. 


pt. 


84 


A8TR0N0MY. 


Pig.  35.— the  MunmiAw  cmciJi. 


To 

BCOpi 

that 

tre( 
the 
plact 
inicr 
form 
Just 
crosf 
whic 
is  d 
the  < 
slidi 
grad 
cout 
bein 
and 
itb: 
If 

cide 
ber 
sion 
U 
oftl 
non 
this 
sere 
plm 
circ 
■woi 
are 
utc( 

din 
the 

(«) 
circ 
poll 
1 
be 
abi 
tun 
of 
thii 
Wl 
seei 
Th( 
sioi 
obi 


THE  MEUIDIAN  CIJiCLE. 


85 


To  determino  the  readings  P,  P',  P',  etc.,  wo  use  the  micro- 
Bcopea  li,  B,  etc.  The  observer,  after  having  set  the  telescope  so 
that  one  of  the  stars  shall  cross  the  field  of  view  exactly  at  its  cen- 
tre (which  may  be  here  marked  by  a  single  horizontal  thread  in 
the  reticle),  goes  to  each  of  the  microscopes  in  succession  and 
places  his  eye  at  A  (see  Pig.  1,  page  86).  He  sees  in  the  field  of  the 
microscope  the  image  of  the  divisions  of  the  graduated  scale  (Fig.  2) 
formed  at  D  (Fig.  1),  the  common  focus  of  the  lenses  A  and  C. 
Just  at  that  focus  is  placed  a  notched  scale  (Pig.  2)  and  two 
crossed  spider  lines.  These  lines  are  fixed  to  a  sliding  frame  a  a, 
which  can  be  moved  by  turning  the  graduated  head  F.  This  head 
is  divided  usually  into  sixty  parts,  each  of  which  is  1 '  of  arc  on 
the  circle,  one  whole  revolution  of  the  head  serving  to  move  the 
sliding  frame  a  o,  and  its  crossed  wires  through  60"  or  1'  on  the 
graduated  circle.  The  notched  scale  is  not  movable,  but  serves  to 
count  the  number  of  complete  revolutions  made  by  the  screw,  there 
being  one  notch  for  each  revolution.  The  index  i  (Pig.  2)  is  fixed, 
and  serves  to  count  the  number  of  parts  of  F  which  are  carried  past 
it  by  the  revolution  of  this  head. 

If  on  setting  the  crossed  threads  at  the  centre  of  the  motion  of 
F  and  looking  into  the  microscope,  a  division  on  the  circle  coin- 
ci'des  with  the  cross,  the  reading  of  the  circle  Pis  the  exact  num- 
ber of  degrees  and  minutes  corresponding  to  that  particular  divi- 
sion on  the  divided  circle. 

Usually,  however,  the  cross  has  been  apparently  earned  pait  one 
of  the  exact  divisions  of  the  circle  by  a  certain  quantity,  which  is 
now  to  be  measured  and  added  to  the  reading  corresponding  to 
this  adjacent  division.  This  measure  can  be  made  by  turning  the 
screw  back  say  four  revolutions  (measured  on  the  notched  scale) 
plus  37-3  parts  rmeasured  by  the  index  t).  If  the  division  of  the 
circle  in  question  was  179°  50',  for  example,  the  complete  reading 
would  be  in  this  case  179'  50'  +  4'  87''. 3  or  179°  64'  87". 3.  Such 
a  reading  is  made  by  each  microscope,  and  the  mean  of  the  min- 
utes and  seconds  from  all  four  taken  as  the  circle  reading. 

We  now  know  how  to  obtain  the  readings  of  our  circle  when 
directed  to  any  point.  We  require  some  zero  of  referencej  as 
the  nadir  reading  (N),  the  polar  reading  (P),  the  equator  reading, 
(Q\  or  the  zenith  reading  (Z)-  Any  one  of  these  being  known,  the 
circle  readings  for  any  stars  as  P.  P',  P",  etc.,  can  be  turned  into 
polar  distances  p',  p",  p'",  etc. 

The  nadir  reading  (N)  is  the  zero  commonly  employed.  It  can 
be  determined  by  pointing  the  telescope  vertically  downward  at 
a  basin  of  mercury  placed  immediately  beneath  the  instrument,  and 
turning  the  whole  instrument  about  the  axis  until  the  middle  wire 
of  the  reticle  seen  directly  exactly  coincides  with  the  in  ^e  of 
this  wire  seen  by  reflection  from  the  surface  of  the  quicksilver. 
When  this  is  the  case,  the  telescope  is  vertical,  as  can  be  easily 
seen,  and  the  nadir  reading  may  be  found  from  the  circles. 
The  meridian  circle  thus  serves  to  determine  both  the  ripht  ascen- 
sion and  declination  of  a  given  star  at  the  same  culmination.  Zone 
observations  are  made  with  it  by  clamping  the  telescope  in  one 


mi 


86 


ASTRONOMY. 


nfti. 


n«.s 


Ti]|.4. 


FlO.    36.— RKADINa  MICR08C0PK,   MICROMETEK  AND   LKVKt. 


dlr 
its 
larj 


pri 
of 
to 
ell 
inf 
eai 
ap 
cei 
eie 
ot] 
wt 
mi 
th 
ax 
(tl 
hx 

ei1 
te 
fo 

kc 
a> 
al 

ti( 
rij 
si: 

ni 
te 


THE  EQUATOJtIAL. 


87 


direction,  and  observing  succossively  the  stars  wliich  ^ass  through 
its  field  of  view.  It  is  by  this  rapid  method  of  observing  that  the 
largest  catalogues  of  stars  have  been  formed. 

§  7.    THE  EQUATORIAL. 

To  complete  the  enumeration  and  description  of  the 
principal  instruments  of  jistronomy,  we  require  an  account 
of  the  eqtiatorial.  This  terra,  properly  speaking,  refers 
to  a  form  of  mounting,  but  it  is  commonly  used  to  in- 
clude both  mounting  and  telescope.  In  this  class  of 
instruments  the  object  to  be  attained  is  in  general  the 
easy  finding  and  following  of  any  celestial  object  whose 
apparent  place  in  the  heavens  is  known  by  its  right  as- 
cension and  declination.  The  equatorial  mounting  con- 
sists essentially  of  a  pair  of  aaes  at  right  angles  to  each 
other.  One  of  these  S  N  (the  jpolar  oasis)  is  directed  to- 
ward the  elevated  pole  of  the  heavens,  and  it  therefore 
makes  an  angle  with  the  horizon  equal  to  the  latitude  of 
the  place  (p.  21).  This  axis  can  be  turned  about  its  own 
axial  line.  On  one  extremity  it  carries  another  axis  Z  D 
(the  declination  <m»),  which  is  fixed  at  right  angles  to  it, 
but  which  can  again  be  rotated  about  its  axial  line. 

To  this  last  axis  a  telescope  is  attached,  which  may 
either  be  a  reflector  or  a  refractor.  It  is  plain  that  such  a 
telescope  may  be  directed  to  any  point  of  the  heavens  ; 
for  we  can  rotate  the  declination  axis  until  the  telescope 
points  to  any  given  polar  distance  or  declination.  Then, 
keeping  the  telescope  fixed  in  respect  to  the  declination 
axis,  we  can  rotate  the  whole  instrument  as  one  mass 
about  the  polar  axis  until  the  telescope  points  to  any  por- 
tion of  the  parallel  of  declination  defined  by  the  given 
right  ascension  or  hour-angle.  Fig.  37  is  an  equatorial  of 
six-inch  aperture  which  can  be  moved  from  place  to  place. 

If  we  point  such  a  telescope  to  a  star  when  it  is  rising 
(doing  this  by  rotating  the  telescope  first  about  its  decli- 
nation axis,  and  then  about  the  polar  axis),  and  fix  the 
telescope  in  this  position,  we  can,  by  simply  rotating  the 


VKIi, 


88 


ASlJiONOMr. 


FlO.  37.— BQUATORIAL  TELEBCOPE  IHIIHTED  TOWAHD  THE  POI-E. 


; 


rilK  MWROMKTRR. 


f 


whole  apparatus  on  the  polar  axis,  cause  the  telescope  to 
trace  out  on  the  celestial  sphere  the  apparent  diurnal  path 
which  tliis  star  will  appear  to  follow  from  rising  to  set- 
ting. In  such  telescopes  a  driving-clock  is  so  arranged 
that  it  can  turn  the  telescope  round  the  polar  axis  at  the 
same  rate  at  which  the  earth  itself  turns  about  its  own  axis 
of  rotation,  but  in  a  contrary  direction.  Hence  such  a 
telescope  once  pointed  at  a  star  will  continue  to  point  at  it 
as  long  as  the  driving-clock  is  in  operation,  thus  enabling 
the  astronomer  to  observe  it  at  his  leisure. 


I  I    lli 


POIiE. 


\ 


FlO.   88.— MKABCBQMBHT  OF  F08ITION-ANGLB. 

Every  equatonal  telescope  intended  for  making  exact  measures 
has  a  JUar  micrometer,  which  is  precisely  the  same  in  principle  as 
the  reading  microscope  in  Fig.  3,  page  86,  except  that  its  two  wires 
are  parallel. 

A  figure  of  this  instrument  is  given  in  Pig.  ?  v  cce  86.  One  of 
the  wires  is  fixed  and  the  other  is  movable  by  >  ha  screw.  To 
measure  the  distance  apart,  of  two  objects  A  and  B,  wire  1  (the 
fixed  wire)  is  placed  on  A  and  wire  2  (movable  by  the  screw)  is 
placed  on  B.  The  number  of  revolutions  and  parts  of  a  revolution 
of  the  screw  is  noted,  say  10' -267  ;  then  wires  1  and  2  are  placed 
in  coincidence,  and  this  zero-reading  noted,  say  5' -143.  The  dis- 
tance A  B  is  equal  to  5'- 124.  Placing  wires  1  and  2  a  known  num- 
ber of  revolutions  apart,  we  may  observe  the  transits  of  a  star  in  the 
equator  over  them  ;  and  from  the  interval  of  time  required  for  this 
star  to  move  over  say  fifty  revolutions,  the  value  of  one  revolution 


90 


AaTRONOMT. 


is  known,  and  can  alwavs  bo  used  to  turn  distances  measured  in 
revolutions  to  distances  in  time  or  arc. 

By  the  filar  micrometer  we  can  determine  the  distance  Hput  in 
seconds  of  arc  of  any  two  stars  A  and  B.  To  completely  nx  the 
relative  position  of  A  and  B,  wo  require  not  only  this  distance,  but 
also  the  angle  which  the  line  A  B  mulces  with  some  fixed  direction 
in  space.  We  assume  as  the  fixed  direction  that  of  the  meridian 
passing  through  A,  Suppose  in  Fig.  88  A  and  £  to  be  two 
stars  visible  in  the  field  of  the  equatorial.  The  clock-work 
is  detached,  and  by  the  diurnal  motion  of  the  earth  the  two 
stars  will  cross  the  field  slowly  in  the  direction  of  the  parallel  of 
declination  passing  through  A,  or  in  the  direction  of  the  arrow  in 
the  figure  from  E.  to  W.,  east  to  west.  The  filar  micrometer  is  con- 
structed so  that  it  can  be  rotated  bodily  about  the  axis  of  the  tele- 
scope, and  a  graduated  circle  measures  the  amount  of  this  rotation. 
The  micrometer  is  then  rotated  until  the  star  A  will  pass  along 
one  of  its  wires.  This  wire  marks  the  direction  of  the  parallel. 
The  wire  perpendicular  to  this  is  then  in  the  meridian  of  the  star. 

The  pontion  angle  of  B  with  respect  to  ^1  is  theh  the  angle  which 
A  B  makes  with  the  meridian  A  N  passing  through  A  toward  the 
north.  It  is  zero  when  B  is  north  of  A,  90*  when  B  is  east,  IHO 
when  B  is  south,  and  270°  when  B  is  west  of  A.  Knowing  p,  the 
position  angle  (NAB  in  the  figure),  and  i  (A  B)  the  distance  of  B, 
we  can  findthe  difference  of  right  ascension  (A  a),  and  the  differ- 
ence of  declination  (hi)  ot  B  from  A  by  the  formulte, 

Aa  =  <  sin |>;  A6=s$  cotp. 

Conversely  knowing  Aa  and  Ad,  we  can  deduce  «  and  p  from 
these  formulae.  The  angle  p  is  measured  while  the  clock-work 
keeps  the  star  A  in  the  centre  of  the  field. 

§  8.    THX   ZnnTH   TBLB800PE. 

The  accompanying  figure  givn  a  view  of  the  zenith  telescope  in 
the  form  in  wuich  it  is  used  by  the  United  States  Coast  Survey.  It 
consists  of  a  vertical  pillar  which  supports  two  T$.  In  these 
rests  the  horizontal  axis  of  the  instrument  which  carries  the  tele- 
scope at  one  end,  and  a  counterpoise  at  the  other.  The  whole  in- 
strument can  revolve  180°  in  azimuth  about  this  pillar.  The  tele- 
scope has  a  micrometer  at  its  eye-end,  and  it  also  carries  a  divided 
circle  provided  with  a  fine  level.  A  second  level  is  provided, 
whose  use  is  to  make  the  rotation  axis  horizontal.  The  peculiar 
features  of  the  zenith  telescope  are  the  divided  circle  and  its  at- 
tached level.  The  level  is,  as  shown  in  the  cut,  in  the  plane  of 
motion  of  the  telescope  (usually  the  plane  of  the  meridian),  and  it 
can  be  independently  rotated  on  the  axis  of  the  divided  circle,  and 
set  by  means  of  it  to  any  angle  with  the  optical  axis  of  the  telescope. 
The  circle  is  divided  from  zero  (0°)  at  its  lowest  point  to  90°  in 
each  direction,  and  is  firmly  attached  to  the  telescope  tube,  and 
moves  with  it. 

By  setting  the  vernier  or  index-arm  of  the  circle  to  any  degree 
and  minute  as  a,  and  clamping  it  there  (the  level  moving  with  it). 


THE  ZKNirU   TKLEtiUOPK. 


n 


d  in 

rt  in 

the 
,  but 
ction 
idian 

two 
work 

two 
lei  of 
9W  in 
I  con- 
I  tele- 
ttion. 
ilong 
rallel. 
}tar. 
which 
d  the 
,  180 
p,  the 
of  B, 
differ- 


>  from 
L-work 


Qope  in 
rey.   It 
1  these 
le  tele- 
liole  in- 
he  tele- 
divided 
ovided, 
peculiar 
[its  at- 
tlane  of 
I,  and  it 
cle,  and 
lescope. 
;o  90°  in 
ibe,  and 

y  degree 
with  it), 


-rtiiiijiljli 

PlO.  89.— THE  ZBNITH  TELBBCOPE. 


Of 


AsTn(tm)MY. 


niul  then  rntatiiiK  thn  tclcscono  and  tho  whnlo  NyMtuin  nlioiit  tliu 
horizontal  axis  until  tlie  bub1>lc  of  the  level  ix  in  tho  contro  of  tlu; 
lovcl-tubo,  tho  axiH  of  the  tolcHcopcH  will  bo  directed  to  the  zenith 
diHtance  a.  The  filar  micromotor  \*  ho  adjusted  that  a  motion  of  itit 
Hcrow  moMurcB  differences  of  zenith  distance.  Tho  uhc  of  tho  ze- 
nith telescope  is  for  determining  tho  latitude  by  Talcott'h 
method.  The  theory  of  this  operation  has  been  already  given  on 
irngo  48.  A  description  of  tho  actual  process  of  observation  will 
illustrate  the  excellences  of  this  method. 

Two  stars,  A  and  B,  are  selected  beforehand  (from  Star  Cata- 
logues), which  culminate,  A  south  of  the  zenith  of  tho  nluce  of  ob- 
servation, B  north  of  it.  They  are  chosen  ot  nearly  eijual  zenith  dis- 
tances f*  and  £*,  and  so  that  $* — {*  is  less  than  tho  breadth  of  tho 
field  of  view.  Their  right  ascensions  are  also  chosen  so  as  to  bo  alwut 
the  same.  The  circle  is  then  set  to  the  mean  zenith  distance  of  the 
two  stars,  and  the  telescope  is  pointed  so  that  the  bubble  is  nearly  in 
the  middle  of  the  level.  Suppose  the  right  ascension  of  A  is  the 
smaller,  it  will  then  culminate  first.  The  telescope  is  then  turned 
to  the  south.  As  A  passes  near  the  centre  of  the  field  its  distance 
from  the  centre  is  measured  by  the  micromotor.  Tho  level  and 
micrometer  are  read,  the  whole  instrument  is  revolved  180",  and 
star  B  is  observ«}d  in  the  same  way. 

By  these  operations  wo  have  determined  the  difference  of  tho 
zenith  distances  of  two  stars  whoso  declinations  d*  and  <)■  uro 
known.     But  tp  being  the  latitude, 

^  =  (J*  -f.  4*  and  ^  =  d"  —  {",  whence 

^  =  !(<)*  +  ')•)  + 1  ({*  - «"). 

The  first  term  of  this  is  known  ;  tho  second  is  measured  ;  so  that 
each  pair  of  stars  so  observed  gives  a  value  of  tho  latitude  which 
depends  on  the  measure  of  n  very  small  arc  with  the  micrometer, 
and  UN  this  arc  can  be  measured  with  great  precision,  the  exactness 
of  the  determination  of  the  latitude  is  equally  great. 


hnruim 
plane  < 
This 
the  in( 
which 
E  is  a 
Hv  it  a 
silverec 
plane  c 


g  8.    THE  SEXTAnr. 

Tho  sextant  is  a  portable  instrument  by  which  tho  altitude!^ 
of  celestial  bodies  or  tho  angular  distances  between  them  mny 
bo  measured.  It  is  used  chiefly  by  navigators  for  determining  the 
latitude  and  the  local  time  of  the  position  uf  tho  ship.  Knowing 
the  local  time,  and  com]}aring  it  with  a  chronometer  regulated  on 
Greenwich  time,  the  longitude  becomes  known  and  the  snip's  place 
is  fixed. 

It  consists  of  the  arc  of  a  divided  circle  urually  00°  in  extent, 
whence  the  name.  This  arc  is  in  fact  divided  into  120  equal  parts, 
each  marked  as  a  degree,  and  these  are  again  divided  into  smaller 
spaces,  so  that  by  means  of  the  vernier  at  the  end  of  tho  index-arm 
M San  arc  of  10"  (usually)  may  be  read. 

The  index-arm  M  8  carries  the  ind«e-ghu»  M,  which  is  a  silvered 
plane  mirror  set  perpendicular  to  the  plane  of  the  divided  arc.  The 


(and  t\ 
second 
to  be  re 
telosco{ 
the  sex 
one  dir 

Tho 
which 
thelaat 


TIIK  SRXTANi:  W 

hnrixim-iihiM  m  is  nlt<(»  n  pliino  mirror  flxp«l    |M!rpcn<lic>ilttr  to  tint 
i»lun<>  oif  tlio  «livi(lf(l  <-inU'. 

TliiH  liiHt  kIiihh  Im  11x1(1  in  poHitixn,  wliilii  (lie  llrnt  rcvolvcH  with 
the  index-unn.  Tlu!  horizon-gliws  in  divided  into  two  piirtH,  «»f 
wJiich  the  lower  one  is  Bilvered,  the  vippcr  Imlf  beinjr  tran»i»«rent. 
E  iH  II  tcleBCope  of  low  power  i>ointu(l  toward  the  horizon-gluiw. 
Hy  it  any  object  to  which  it  Ih  directed  can  Iw  seen  through  tlic  un- 
Bilvcrcd  half  of  the  horizon-glawH.  Any  other  object  in  the  f«anio 
pUnu  can  be  brought  into  the  same  field  by  rotating  the  indpx-arm 


FfO.  40. — THB  BKXTAHT. 

(and  the  index-glass  with  it),  so  that  a  beam  of  light  from  this 
second  object  shall  strike  the  index-glass  at  the  proper  angle,  there 
to  be  reflected  to  the  horizon-glass,  and  again  reflected  down  the 
telescope  E.  Thus  the  images  of  any  two  objects  in  the  plane  of 
the  sextant  may  be  brought  together  in.  the  telescope  by  viewing 
one  directly,  and  the  other  by  reflection. 

The  principle  upon  which  the  sextant  depends  is  the  following, 
which  IS  proved  in  optical  works.  The  artgle  between  theftnt  and 
the  latt  directum  of  a  ray  which  hat  suffered  two  rejUetiont  in  the  tame 


Vv 


ASTRONOMY. 


\ 


plans  M  equal  to  tt^^s  the  angle  whkh  tTu  two  reflecting  mrfaeea  make 

with  each  other.  .     . ,     ,  ,       a  *».;„  ,o„  Sa  i.tr 

In  the  figure  S  A  is  the  ray  incident  upon  -4,  and  this  ray  is  by 

reflection  brought  to  the  direction  BE     The  theorem  declares 

that  the  angle  BE  Sis  equal  to  twice  D  C  B,  or  tvice  the  angle  of 


theiairrors,  since  BO  mAD  Care  perpendicular  to  Band  ^.  To 
measure  the  altitude  of  a  star  (or  the  sun)  at  sea,  the  sextant  is  held 
in  the  hand,  and  the  telescope  is  pointed  to  the  sea-honzon,  which 
appears  like  a  definite  line.  The  index-arm  is  then  moved  until 
the  reflected  image  of  the  sun  or  of  the  star  coincidcB  with  the 


Fie.   43.— ABTIVTCIAL  HOBOOK. 


imaee  of  the  sea-horizon  seen  directly.  When  this  occurs  the  tune 
isto  be  D  ied  from  a  chronometer.  If  a  star  is  observed,  the  reaa- 
injr  of  the  divided  limb  gives  the  altitude  directly;  if  it  is  the 
sun  or  moon  which  has  been  observed,  the  lower  limb  of  these  is 
brought  to  coincide  with  the  horizon,  and  the  altitude  of  the  centre 


is  found 
Almanac 

The  an 
ured  by  j 
tant  abou 
vided  arc 
the  indes 
star's  imi 

On  shn 
tho  obsei 
hffrigon,  ' 
liquid,  a 
surface  if 
a  A,  fror 
in  the  di 
ing  E  A 
to  an  eye 
With  a  » 
angle  8 
and  if  A 
all  celest 
will  equi 
half  the  i 


i  mahe 

y  isby 
eclarea 
ngle  of 


A.  To 
:  is  held 
,  which 
id  until 
nth  the 


THE  8KXTANT. 


96 


is  found  by  applying  the  semi-diameter  as  found  Jn  the  Nautical 
Almanac  to  the  observed  altitude  ol  the  limb. 

The  angular  distance  apart  of  a  star  and  the  moon  can  be  meas- 
ured by  pointing  the  telescope  at  the  star,  revolving  the  whole  sex- 
tant about  the  sight-line  of  the  telescope  until  the  plane  of  the  di- 
vided arc  passes  through  both  star  and  moon,  and  then  by  moving 
the  index-arm  until  the  reflected  moon  is  just  in  contact  with  the 
star's  image  seen  directly. 

On  shore  the  horizon  is  broken  up  by  buildings,  trees,  etc.,  and 
tho  observer  is  therefore  obliged  to  have  recourse  to  an  artificial 
harum,  which  consists  usually  of  the  reflecting  surface  of  some 
liquid,  as  mercury,  contained  in  a  small  vessel  A,  whose  upper 
surface  is  necessarily  parallel  to  the  horizon  DAG.  A  ray  of  light 
8  A,  from  a  star  at  8,  incident  on  the  mercury  at  A,  will  be  reflected 
in  the  direction  A  E,  making  the  angle  8AG=  0  A  8'  (A  8^  be- 
ing E  A  produced),  and  the  reflected  image  of  the  star  will  appear 
to  an  eye  at  £  as  far  below  the  horizon  as  the  real  star  is  above  it. 
With  a  sextant  whose  index  and  horizon-masses  are  at  /and  H,  the 
angle  8  E  8  may  be  measured  ;  but  aES  =  8AS  —  A8E, 
ana  it  A  E'vi  exceedingly  small  as  compared  with  ^  i8,  as  it  is  for 
all  celestial  bodies,  the  angle  A  8  Emaj  be  weglected,  and  8  B  8' 
will  equal  8  A  8',  or  double  the  altitude  of  the  object :  hence  one 
half  the  reading  of  the  instrument  will  give  the  apparent  altitude. 


the  time 
the  read- 
it  is  the 
these  is 
he  centre 


\ii 


Hi 


'■'I 


§1. 


CHAPTER  III. 

MOTION    OF   THE   EARTH. 
ANCIENT  IDEAS  OF  THE  PLANETS. 


It  was  obBerved  by  the  ancients  that  while  the  great 

mass  of  the  stars  maintained  their  positions  relatively  to 

Lh  other  not  only  during  each  diurnal  revolution,  but 

^nth  after  month  and  year  after  year,  the«,  were  vi«. 

bleto  them  seven  l^eavenly  bodi^  which  ch^gedth^r 

positions  relatively  to  the  starB  and  to  «««'5^^f  «^.  J^,^ 

Siey  called  planets  or  wandenng  stars.     Still  calbng  the 

apmi^t   crystalline  vault   in  which  the  sters  seem  to 

^^  the  celestial  sphere,  and  imagining  it  as  at  rest, 

^wt  found  that  the  seven  planets  performed  a  y^ 

slow  revolution    around  the  sphere  from  west  to  e.«t 

L  periods  ranging  from  one  month  in  the  case  of  the 

mooTto  thirtyVars  in  that  of  m^n.     1*  w-  eviden 

that  these  bodies  could  not  be  «o"«^«'«'l.  ^^  ^*  ^  not 
same  solid  sphere  with  the  stars,  because  tW  could^no 
then  change  their  positions  among  the  stars.  Vanous 
w^s  of  acfounting  for  their  motions  were  therefore  pro- 
xJed  One  of  the  earliest  conceptions  is  associated  with 
rnameofPvTHAOOKAS.     He  is  said  to  have  taugM  t^t 

each  of  the  seven  planets  had  its  ^^/P^^^^^^^^t^j 
concentric  with  that  of  the  fixed  stars,  and  that  these 
len  hoUow  spheres  each  performed  its  own  revolution, 
Se^ndently  of  theothers.  Thisideaof  anumber  of  con- 
3c  solid^heres  was,  however,  apparently  given  up 


without 

argumci 

close  ex 

tent  wit 

being  » 

perfect i 

by  the 

The  latl 

move  so 

it  was  ( 

nearer  \ 

were  en 

fixed  in 

use — th( 

space  or 

These 

lowed,  \ 

rightly  < 

stars.     ] 

most  slo 

distance 

case  of  J 

We  n 

the  eart! 

scope  ha 

themseh 

ably  grei 

surface  I 

pared  wi 

stars.     1 

tem,  it  if 

its  sever 

them  thi 

following 

to  be  eij 

in  the  o 

bodies  a 


STB. 

the  great 
atively  to 
ution,  but 
were  visi- 
iged  their 
r.     These 
ailing  the 
I  seem  to 
18  at  rest, 
id  a  very 
t  to  east, 
ase  of  the 
ras  evident 
set  in  the 

could  not 
.  Various 
•efore  pro- 
ciated  with 
taught  that 
iside  of  and 

that  these 
revolution, 
iber  of  con- 
f  given  up 


THE  SOLAR  SYSTEM. 


W 


without  any  one  having  taken  tlie  trouble  to  refute  it  by 
argument.  Although  at  first  sight  plausible  enough,  a 
close  examination  would  show  it  to  be  entirely  inconsis- 
tent with  the  observed  facts.  The  idea  of  the  fixed  stars 
being  set  in  a  solid  sphere  was,  indeed,  in  seemingly 
perfect  accord  with  their  diurnal  revolution  as  observed 
by  the  naked  eye.  But  it  was  not  so  with  the  planets. 
The  latter,  after  continued  observation,  were  found  to 
move  sometimes  backward  and  sometimes  forward  ;  and 
it  was  quite  evident  that  at  certain  periods  they  were 
nearer  the  earth  than  at  other  periods.  These  motions 
were  entirely  inconsistent  with  the  theory  that  they  were 
fixed  in  solid  spheres.  Still  the  old  language  continued  in 
use — the  word  sphere  meaning,  not  a  soUd  body,  but  the 
space  or  region  within  which  the  planet  moved. 

These  several  conceptions,  as  well  as  those  which  fol- 
lowed, were  all  steps  toward  the  tnith.  The  planets  were 
rightly  considered  as  bodies  nearer  to  us  than  the  fixed 
stars.  It  was  also  rightly  judged  that  those  which  moved 
most  slowly  were  the  most  distant,  and  thus  their  order  of 
distance  from  the  earth  was  correctly  given,  except  in  the 
case  of  Mercury  and  Venus. 

We  now  know  that  these  seven  planets,  together  with 
the  earth,  and  a  number  of  other  bodies  which  the  tele- 
scope has  made  known  to  us,  form  a  family  or  system  by 
themselves,  the  dimensions  of  which,  although  inconceiv- 
ably greater  than  any  which  we  have  to  deai  with  at  the 
surface  of  the  earth,  are  quite  insignificant  when  com- 
pared with  the  distance  which  separates  us  from  the  fixed 
stars.  The  sun  being  the  great  central  body  of  this  sys- 
tem, it  is  called  the  Solar  System.  It  is  to  the  motions  of 
its  several  bodies  and  the  consequences  which  flow  from 
them  that  the  a  oention  of  the  reader  is  directed  in  the 
following  chapters.  We  premise  that  there  are  now  known 
to  be  eight  lai^  planets,  of  which  the  earth  is  the  third 
in  the  order  of  distance  from  the  sun,  and  that  these 
bodies  all  perform  a  regular  revolution  around  the  son. 


■ 


98  ASTRONOMY. 

Mercnry,  the  nearest,  performs  its  revolution   in  three 
montlis  ;  Neptune,  the  farthest,  in  164  yea". 

First  n  importance  to  us,  among  the  heavenly  boU  es 
which  we  see  from  the  earth,  stands  the  sun,  the  supporter 
rS  and  motion  upon  theearth.  At  fi«t«ghUUm^ 
seem  curious  that  the  sun  and  seemmg  stars  like  Ma/rs 
and^a  Cm  should  have  been  classified  together  as  plajete 
bv  the  ancients,  while  the  fixed  stars  were  considered  as 
forming  anoth;r  class.       That  the  ancients  were  acute 

Z^f  to  do  this  tends  to  impr^  m  wHh  a  favorable 
sense  of  the  scientific  character  of  their  mteUect  To  any 
but  the  most  careful  theorists  and  observers,  the  star-like 
pknete  if  we  may  call  them  so,  would  never  have  seemed 
rSng  in  the  Ime  class  with  the  sun  but  rather  m 

hat  of  tie  stars  ;  especially  when  it  ^^^^^^^^  '^' '^^ 
were  never  visible  at  the  same  time  with  the  sun.  iJut 
Srthe  times  of  which  we  liave  any  histenc  r^rd 
there  were  men  who  saw  that,  in  a  motion  from  west  to 
rramong  the  fixed  stars,  these  several  ^^^  ^^^^J 
common  character,  which  was  more  ««««^*^^.2;^  ^^^^ 
of  the  universe  than  were  their  immense  diforences  of 

aspect  and  lustre,  striking  tl^o^g^^.J^'fl^^-^  ,„_ 
It  must,  however,  be  remembered  ^^^^J^^^^ 
consider  the  sun  as  a  planet.     We  have  /no^^^f  *^«  "^ 
dent  system  by  making  the  sun  and  the  earth  /jhaage 
llrso  that  the  latterl  now  regarded  as  one  of  theei^t 
wTiknets,  while  the  former  has  taken  the  place  of  the 
e^Kfientral  body  of  the  system     In  consequence 
oUhe  revolntion  of  the  planets  romid  Jbe  "an  «ach  of 
them  seems  to  perform  a  corresponding  circuit  m  the 
htvenriund  Se  celestial  sphere,  when  viewed  from 
any  other  phmet  or  from  the  earth. 
§  2.    AMlfUAL  EBVOLTJTIOM  OF  THE  BABTH. 
To  an  observer  on  the  earth,  the  sun  seems  to  pe^o^f 
Jua^volution  among  the  stars  a  fact  v.hich  has  b^n 
Wn  from  the  earUest  ages.    We  now  know  that  this 


is  due 
sun. 
tion  oi 
directe 
it  and 
which 
In  ] 
of  the 


fixed 
tent,  1 
AB 
numb 
15  dn 
called 
exten 
the  p 


MOTION  OF  TBE  BARTB. 


99 


is  due  to  the  annual  revolution  of  the  earth  round  the 
Bun.  It  is  to  the  nature  and  eflfects  of  this  annual  revolu- 
tion of  the  earth  that  the  attention  of  the  reader  is  now 
directed.  Our  first  lesson  is  to  show  the  relations  between 
it  and  the  corresponding  apparent  revolution  of  the  sun, 
which  is  its  counterpart. 

In  Fig.  43,  let  S  represent  the  sun,  ABC  D  the  orbit 
of  the  earth  around  it,  and  EFQIl  tlie  sphere  of  the 


Fia.  43.— BRVOLCTioN  or  thb  earth. 

fixed  stars.  This  sphere,  being  supposed  infinitely  dis* 
tent,  must  be  considered  as  infinitely  larger  than  the  circle 
A  B  G  D.  Suppose  now  that  1,  2,  3,  4,  5,  6  are  a 
number  of  consecutive  positions  of  the  earth.  The  line 
\S  drawn  from  the  sun  to  the  earth  in  the  first  position  is 
called  the  radius  vector  of  the  earth.  Suppose  this  line 
extended  infinitely  so  as  to  meet  the  celestial  sphere  in 
the  point  V.    It  is  evident  that  to  an  observer  on  the 

tofO. 


jQO  ASTRONOMY. 

y  ;^Tr«:'aLtI  »«  .Sana  so„„.     in  other 
Will  ^PP""  ,    rnvolves  around  the  sun,  the  latter 

-''itr=rre^;r.:'r>rt-,.  .o.a 

described.  „„„„„i  mvolntion  of  the 

Let  us  now  study  the  apparent  ^^^'^'^Xe  i^ult  of 
«„n  produced  in  the  way  just  mentioned.     One  result 


TUE  aUN'B  APPARENT  PATH. 


101 


>liere 
2,  it 
other 
latter 
Btars, 

inrould 
xactly 
i  from 
dly  in 
t  that 
ng  the 
irately 

rse  de- 
ited  by 
iiity  in 
eat  cir- 
pear  to 
ndiffer- 
iptic  is 
the  po- 
eferred. 
letry,  it 
a  think- 
ceive  of 
ical  line 
perpen- 
Rgure  is 
iects  the 
c.     This 
Ets  an  ex- 
j,  owing 
hereafter 

on  of  the 
result  of 


this  motion  is  probably  familiar  to  every  reader,  in  the 
different  constellations  whicli  are  seen  at  different  times  of 
the  year.  Let  lis  take,  for  example,  the  bright  star  Aide- 
baran,  wliicli,  on  a  winter  evening,  we  may  see  north- 
west  of  Orion.  Near  the  end  of  February  this  star  crosses 
the  meridian  about  six  o'clock  in  the  evening,  and  sets 
about  midnight.  If  we  watch  it  night  after  night  through 
the  months  of  March  and  April,  we  shall  find  that  it  is  far- 
ther and  farther  toward  the  west  on  each  successive  even- 
ing at  the  same  hour.  By  the  end  of  April  we  sliall  bare- 
ly be  able  to  see  it  about  the  close  of  the  evening  twilight. 
At  the  end  of  May  it  will  be  so  close  to  the  sun  as  to  be 
entirely  invisible.  This  showa.  that  during  the  months  we 
have  been  watching  it,  the  sun  has  been  approaching  the 
star  from  the  west.  If  in  July  we  watch  the  eastern 
horizon  in  the  early  morning,  we  shall  see  this  star  rising 
before  the  sun.  The  sun  lias  therefore  passed  by  the 
star,  and  is  now  east  of  it.  At  the  end  of  November  we 
will  find  it  rising  at  sunset  and  setting  at  ennrise.  The 
sun  is  therefore  directly,  opposite  the  star.  During  the 
winter  months  it  approaches  it  again  from  the  west,  and 
passes  it  about  the  end  of  May,  as  before.  Any  other 
star  south  of  the  zenith  shows  a  similar  change,  since  the 
relative  positions  of  the  stars  do  not  vary. 

§  3.    THE   SUV'S   AFPASEirF  PATH. 

It  is  evident  that  if  the  apparent  path  of  the  sun  lay  in 
the  equator,  it  would,  during  the  entire  year,  rise  exactly 
in  the  east  and  set  in  the  west,  and  would  always  cross 
the  meridian  at  the  same  altitude.  The  days  would 
always  be  twelve  hours  long,  for  the  same  reason  that  a 
star  in  the  equator  is  always  twelve  hours  above  the  hori- 
zon and  twelve  hours  below  it.  But  we  know  that  this 
is  not  the  case,  the  sun  being  sometimes  north  of  the 
equator  and  sometimes  south  of  it,  and  therefore  having 
a  motion  in   declination.      To  understand  this  motion. 


XOa  ASriiONOMY. 

8unix«e  that  on  March  19th,   1879,  the  Bun  had  been 
observed  with  a  meridian  circle  and  a  Biderca,!  clock  at  the 
moment  of  transit  over  the  meridian  of  Wa«hnigton.     Its 
position  would  have  been  found  to  bo  this  : 
Eight  Ascension,  23"  55™  23' ;  Declination,  0"  30'  south. 

Had  the  observation   been  repeated  on  the  20th  and 
following  days,  the  results  would  have  been  : 

March  20,  R.  Ascen.  23"  59™    2';  Dec.  0°    6'  South. 
2 J  u  0"    2™  40";     "    0°  17' North. 

22'         "  0"    C™  19* ;     "    0°  41'  North. 


Fio. 


44.— THB  BOH  CROfltniO  THB  BQUATOB. 


If  we  lay  these  positions  down  on  a  chart,  we  shall  find 
them  to  be  as  in  Fig.  44,  the  centre  of  the  sun  being 
south  of  the  equator  in  the  first  two  positions,  and  north 
of  it  in  the  last  two.  Joining  the  successive  positions  by 
a  line,  we  shall  have  a  small  portion  of  the  apparent  path 
of  the  sun  on  the  celestial  sphere,  or,  in  other  words,  a 
small  part  of  the  ecliptic.  ^v.  *  *i. 

It  is  clear  from  the  observations  and  the  figure  that  the 
sun  crossed  the  equator  between  six  and  seven  o'clock  on 
the  afternoon  of  March  20th,  and  therefore  that  the  equa- 
tor and  ecliptic  intersect  at  the  point  where  the  sun  was  at 
that  hour.     This  point  is  called  the  verrud  e^mnox,  the 


TUB  SUN'S  APPAUKNT  PATH. 


IW 


been 

it  the 

Itg 

louth. 
1  and 

ith. 
rth. 
•rth. 


ai  find 
being 
i  north 
ions  by 
nt  path 
^ords,  a 

;hat  the 
lock  on 
le  eqna- 
i  was  at 
UKC,  the 


first    word    indicating    the    eeason, 
cxpreflscs  the  equality  of  the 
nights  and  days  which  occurs 
when  the  sun  is  on  the  equator. 
It  will  be  remembered  that  this 
equinox  is  the  point  from  wliich 
right  ascensions  are  counted  in 
the  heavens  in  the  same  way 
that  longitudes  on  the  earth  are 
counted    from    Greenwich    or 
Washington.     The  sidereal 
clock  is  therefore  so  set  that 
the  hands  shall  read  0  hours 
0   minutes    0   seconds   at   the 
moment  when  the  vernal  equi- 
nox crosses  the  meridian. 

Continuing  our  observations 
of  the  sun's  apparent  course  for   fe 
c:v   m/inflia   fiTtm  Mftnth  20th    ^ 


while    the    second 


six  months  from  March  20th 
till  September  23d,  we  should 
find  it  to  be  as  in  llg.  45.     It 
will  be  seen  that  Fig.  44  cor- 
responds to  the  right-hand  end 
of  45,  but  is  on  a  much  larger 
scale.     The  sun,  moving  along 
the  great  circle  of  the  ecliptic, 
will  reach  its  greatest  northern 
declination    about    June  2l8t. 
This  point  is  indicated  on  the 
figure  as  90°  from  the  vernal 
equinox,  and  is  called  the  sum- 
iner  solstice.     The  sun's  right 
ascension  is  then  six  hours,  and 
its  declination  23i°  north. 

The  course  of  the  sun  now 
inclines  toward  the  south,  and 
it  again  crosses  the  equator   about  September  Sad  at 


104 


ASTRONOMY. 


a  point  diametrically  opposito  the  vernal  equinox.  In 
virtue  of  the  theorem  of  spherical  trigonometry  that  all 
great  circles  intersect  each  other  in  two  opposite  points, 
the  ecliptic  and  equator  intersect  at  the  two  opposite  equi- 
noxes. The  equinox  which  the  sun  crosses  on  September 
22d  is  called  the  autumnal  equinox. 

During  the  six  months  from  Septemher  to  March  the 
sun's  course  is  a  counterpart  of  that  from  March  to  Sep- 
tember, except  that  it  hes  south  of  the  equator.  It  at- 
tains its  greatest  south  declination  about  December  22d, 
in  right  ascension  18  hours,  and  south  declination  234°. 
This  point  is  called  the  winter  soUtice.  It  then  begins  to 
incline  its  course  toward  the  north,  reaching  the  vernal 
equinox  again  on  March  20th,  1880. 

The  two  equinoxes  and  the  two  solstices  may  be  re- 
garded as  the  four  cardinal  points  of  the  sun's  apparent 
annual  circuit  around  the  heavens.  Its  passage  through 
these  points  is  determined  by  measuring  its  altitude  or 
declination  from  day  to  day  with  a  meridian  circle.  Since 
in  our  latitude  greater  altitudes  correspond  to  greater 
declinations,  it  follows  that  the  summer  solstice  occurs  on 
the  day  when  the  altitude  of  the  sun  is  greatest,  and  the 
winter  solstice  on  that  when  it  is  least.  The  mean  of 
these  altitudes  is  that  of  the  equator,  and  may  therefore 
be  found  by  subtracting  the  latitude  of  the  place  from 
90°.  The  time  when  the  sun  reaches  this  altitude  going 
north  marks  the  vernal  equinox,  and  that  when  it  reaches 
it  going  south  marks  the  autumnal  equinox. 

These  passages  of  the  sun  through  the  cardinal  points 
have  been  the  subjects  of  asti-onomical  observation  from 
the  earliest  ages  on  account  of  their  relations  to  the  change 
of  the  seasons.  An  ingenious  method  of  finding  the  time 
when  the  sun  reached  the  equinoxes  was  used  by  the  as- 
tronomers of  Alexandria  about  the  beginning  of  our  era. 
In  the  great  Alexandrian  Museum,  a  large  ring  or  wheel 
was  set  up  parallel  to  the  plane  of  the  equator— in  other 
words,  it  was  so  fixed  that  a  star  at  the  pole  would  shine 


1 


'_^X^ 


THE  ZODIAC. 


106 


»x.  In 
that  all 
points, 
te  equi- 
ptumber 

ircli  the 
to  Sep- 
,  It  at- 
)6r  22d, 
on  234°. 
)eginB  to 
e  vernal 

y  be  re- 
apparent 

through 
itude  or 
I.  Since 
I  greater 
xscnrs  on 

and  the 
mean  of 
therefore 
ace  from 
ide  going 
it  reaches 

al  points 
tion  from 
le  change 
;  the  time 
by  the  as- 
f  our  era. 
or  wheel 
—in  other 
)uld  shine 


1 


perpendicularly  on  the  wheel.  Evidently  its  plane  if 
extended  must  have  passed  through  the  cast  and  west 
points  of  the  horizon,  while  its  inclination  to  the  vertical 
was  equal  to  the  latitude  of  the  place,  which  was  not  far 
from  30°.  When  the  sun  reached  the  equator  going  north 
or  south,  and  shone  upon  this  wheel,  its  lower  edge  would 
be  exactly  covered  by  the  shadow  of  the  upper  edge  ; 
whereas  in  any  other  position  the  sun  would  shine  upon 
the  lower  inner  edge.  Thus  the  time  at  which  the  sun 
reached  the  equinox  could  be  determined,  at  least  to  a 
fraction  of  a  day.  By  the  more  exact  methods  of  modem 
times,  it  can  be  determined  within  less  than  a  minute. 

It  will  bo  seen  that  this  method  of  determining  the  an- 
nual apparent  course  of  the  sun  by  its  declination  or  alti- 
tude is  entirely  independent  of  its  relation  to  the  fixed 
stars ;  and  it  could  be  equally  well  applied  if  no  stars 
were  ever  visible.  There  are,  therefore,  two  entirely  dis- 
tinct ways  of  finding  when  the  sun  or  the  earth  has  com- 
pleted its  apparent  circuit  around  the  celestial  sphere  ; 
the  one  by  the  transit  instrument  and  sidereal  clocV,  which 
show  when  the  sun  returns  to  the  same  position  among 
the  stars,  the  other  by  the  measurement  of  altitude,  which 
shows  when  it  returns  to  the  same  equinox.  By  the  for- 
mer method,  already  described,  we  conclude  that  it  has 
completed  an  annual  circuit  when  it  returns  to  the  same 
star  ;  by  the  latter  when  it  returns  to  the  same  equinox. 
These  two  methods  will  give  slightly  different  results  for 
the  length  of  the  year,  for  a  reason  to  bo  hereafter 
described.  • 

The  Zodiac  and  its  Diviaioiia. — The  zodiac  is  a  belt 
in  the  heavens,  commonly  considered  as  extending  some  8° 
on  each  side  of  the  ecliptic,  and  therefore  about  16°  wide. 
The  planets  known  to  the  ancients  are  always  seen  within 
this  belt.  At  a  very  early  age  the  zodiac  was  mapped  out 
into  twelve  signs  known  as  the  signs  of  the  zodiac^  the 
names  p£  which  have  been  handed  down  to  the  present 
time.    Each  of  these  signs  was  supposed  to  be  the  seat  of 


loe 


AsmoNimr. 


■«»»> 


a  conftoUation  after  whicli  it  wa«  calUui  Oommcncmg 
it  the  vorruvl  ciuinox,  tho  tt«t  thirty  dogrc«8  through 
whchtroHun  i,La,orth«  region  a.no..g  the  «tar8  m 
whic  it  wa8  ou.ul  during  tlie  m<mth  following,  wan 
Ta^lod  the  In  ArieM.  The  next  thirty  degrees  w.«  called 
SJT  The  nanicB  of  all  the  twelve  «gnB  u.  the^ 
proper  order,  with  the  approximate  time  of  the  buu  «  en- 
tering  upon  each,  are  a»  follow  : 


Arieti,  the  Ram, 
Taurus,  the  Bull, 
Gemmh  the  Twins, 
Camer,  the  Crab, 
Leo,  the  Lion, 
F//yw,  the  Virgin, 
Libra,  the  Balance, 
Scorpin4t,  the  Scorpion, 
Sagittarius,  the  Archer, 
Capricornm,  the  Goat, 
yljMartt**,  the  Wator-l)earer, 
Pi»ce«,  the  Fishes, 


March  20. 
April  20. 
May  20. 
Juno  21. 
Julv  22. 

ft 

August  22. 
Septemlwr  22. 
October  23. 
Noveml)er  23. 
December  21. 
January  20. 
February  19. 


Each  of  these  signs  coincides  roughly  with  a  conste  a- 
tion  in  the  heavens  ;  and  thus  there  are  twelve  constella- 
tions called  by  the  names  of  these  signs,  but  the  signs  and 
the  constellations  no  longer  correspond.  Although  the  sun 
now  crosses  the  equator  and  enters  the  m^r^  Anes  on  the 
20th  of  March,  he  does  not  reach  the  comteUatwn  Anes 
nntil  nearly  a  month  later.  This  arises  from  the  preces- 
sion of  the  equinoxes,  to  be  fxplained  hereafter. 

§  4.    OBLIQUITY  OP  THE  BCLIPTIO. 

We  have  already  stated  that  when  the  sun  is  at  the 
Bommer  solstice,  it  is  about  23*°  north  of  the  equator, 
and  when  at  the  winter  solstice,  about  23i°  south.  This 
Bhow.  that  the  ecliptic  and  equator  make  an  angle 
of    about  23i°  with  each  other.     This  angle  ifl  caUed 


the 
v«r 

ol>H( 

suit 
the 
mui 
will 
tim 
abo 
sevi 
the 

BCV 

on 

tw^t 

1 

son 

tor 

isp! 

is  s 

cell 

In 

vei 

hal 

isp 

to 

soi 

fai 

en 

It 

lat 

is, 

be 

BU 

in 
Tl 
o\ 


1 


onuqvirr  of  riiK  Kvuprra. 


107 


incing 
rough 
aro  in 
,  waH 
callod 
I  their 
i'b  eu- 


•nstella- 
»nBtella- 
gns  and 
the  Bun 
I  on  the 
m  Aries 
preces- 


8  at  the 
equator, 
li.  This 
kU  angle 
IB  called 


the  obliquity  of  (lie  ocliptit ,  iirid  its  dotonnination  ia 
very  siinpk'.  It  is  onlv  necesBary  to  find  by  repeated 
oiwervation  tin  tiun's  greato«t  north  declination  at  the 
eutnnier  Bolstice,  and  its  greatest  south  declination  at 
the  winter  aolstice.  Either  of  these  decliimtions,  which 
must  bo  equal  if  the  olworvations  are  accurately  made, 
will  give  the  obliquity  of  the  ecliptic.  It  has  iMjen  con- 
tinually diminishing  from  the  earliest  ages  at  a  rate  of 
about  half  a  Becond  a  year,  or,  more  exactly,  about  forty- 
seven  seconds  in  a  century.  This  diminution  is  due  to 
the  gravitating  forces  of  the  planets,  and  will  continue  for 
several  thousand  yearn  to  come.  It  will  not,  however,  go 
on  indefinitely,  but  the  obliquity  will  only  oscillate  be- 
tween comparatively  narrow  limits. 

The  relation  of  the  obliquity  of  the  ecliptic  to  the  Bea- 
Bons  is  quite  obvious.     When  the  sun  is  north  of  the  equa- 
tor,  it  culminates  at  a  higher  altitude  in  the  northern  hem- 
isphere, and  more  than  half  of  ita  apparent  diurnal  course 
is  above  the  horizon,  as  explained  in  the  chapter  on  the 
celestial  sphere.     Hepce  we  have  the  heats  of  summer. 
In  the  southern  hemisphere,  of  course,  the  case  is  re- 
veraeu  :  when  the  sun  is  in  north  declination,  less  than 
half  of  his  diurnal  course  is  above  the  horizon  in  that  hem- 
isphere.    Therefore  this  situation  of  the  sun  corresponds 
to  summer  in  the  northern  hemisphere,  and  winter  in  the 
southern  one.     In  exactly  the  same  way,  when  the  sun  is 
far  south  of  the  equator,  the  days  are  shorter  in  the  north- 
em  hemisphere  and  longer  in  the  southern  hemisphere. 
It  is  therefore  winter  in  thft  former  and  summer  in  the 
latter.     If  the  equator  and  the  ecliptic  coincided— that 
is,  if  the  sun  moved  along  the   equator— there  would 
be  no  such  thing  as  a  difference  of  seasons,  because  the 
sun  would  always  rise  exactly  in  the  east  and  set  exactly 
in  the  west,  and  always  culminate  at  the  same  altitude. 
The  days  would  always  be  twelve  hours  long  the  world 
over.     This  is  the  case  with  the  planet  Jupiter. 
In  the  preceding  paragraphs,  we  have  explained  the 


108 


ASTRONOMY. 


apparent  annual  circuit  of  the  sun  relative  to  the  equator, 
and  shown  how  the  seasons  depend  upon  this  circuit.  In 
order  that  the  student  may  clearly  grasp  the  entire  subject, 
it  is  necessary  to  show  the  relation  of  these  apparent  move- 
ments to  the  actual  movement  of  the  earth  around  the 

sun. 

To  understand  the  relation  of  the  equator  to  the  eclip- 
tic, we  must  remember  that  the  celestial  pole  and   the 
celestial  equator  have  really  no  reference  whatever  to  the 
heavens,  but  depend  solely  on  the  direction  of  the  earth  s 
axis  of  rotation.     The  pole  of  the  heavens  is  nothing 
more  than  that  point  of  the  celestial  sphere  toward  which 
the  earth's  axis  points.     If  the  direction  of  this  axis 
changes,  the  position  of  the  celestial  pole  among  the  stars 
will  change  also  ;  though  to  an  observer  on  the  earth, 
unconscious  of  the  change,  it  would  seem  a&  if  the  starry 
sphere  moved  while  the  pole  remained  at  rest.    Again,  the 
celestial  equator  being  merely  the  great  circle  in  which  the 
pkne  of  the  earth's  equator,  extended  out  to  infimty  in 
every  direction,  cuts  the  celestial  sphere,  any  change  in 
the  direction  of  the  pole  of  the  earth  necessarily  changes 
the  position  of  the  equator  among  the  stars.     Now  the 
positions  of  the  celestial  pole  and  the  celestial  equator 
among  the  stars  seem  to  remain  unchanged  throughout 
the  year.    (There  is,  indeed,  a  minute  change,  but  it  does 
not  affect  our  present  reasoning.)    This  shows  th•^t,  as 
the  earth  revolves  around  the  sun,  its  axis  is  constantly 
directed  toward  nearly  the  same  pohit  of  the  celestial 
sphere. 

§  5.    THE  8EA80IV8. 

The  conclusions  to  which  we  are  thus  led  respecting 
the  real  revolution  of  the  earth  are  shown  in  Fig.  46. 
Here  S  represents  the  sun,  with  the  orbit  of  the  earth 
surrounding  it,  but  viewed  nearly  edgeways  so  as  to  be 
much  foreshortened.  ABGD  are  the  four  cardina 
positions  of  the  earth  which  correspond  to  the  cardinal 


poll 
In< 
nor 


san 

it  i 

Ag 
the 
inc 
] 
sur 
noi 
dai 
son 
an| 
wi 
the 
thi 
ilh 
m( 

gl« 
pe 

tk 


ator, 
In 
ject, 
love- 
l  the 

jclip- 
the 

0  the 
irth'a 
thing 
vhich 
>  axis 

1  stars 
sarth, 
starry 
a,  the 
ihthe 
ity  in 
ige  in 
langes 
w  the 
juator 
ighout 
t  does 
•\t,  as 
itantly 
ilestial 


tecting 
ig.  46. 
i  earth 
I  to  be 
ardinal 
ordinal 


THE  SEASONS. 


109 


points  of  the  apparent  path  of  the  sun  ah*eady  described. 
In  each  figure  of  the  earth  J/'S  is  the  axis,  iT  being  its 
north  and  S  its  south  pole.     Since  this  axis  points  in  the 


FlO.   46.— CAV8B8  OF  THK  8BA80NB. 

same  direction  relative  to  the  stars  during  an  entire' year, 
it  follows  that  the  different  lines  N  S  Are  all  parallel. 
Again,  since  the  equator  does  not  coincide  with  the  ecliptic, 
these  lines  are  not  perpendicular  to  the  ecliptic,  but  are 
inclined  from  this  perpendicular  by  23i°. 

Now,  consider  the  earth  as  at  ^  ;  here  it  is  seen  that  the 
sun  shines  more  on  the  southern  hemisphere  than  on  the 
northern  ;  a  region  of  23^°  around  the  north  pole  is  in 
darkness,  while  in  the  corresponding  region  around  the 
south  pole  the  sun  shines  all  day.  The  five  circles  at  right 
angles  to  the  earth's  axis  are  the  parallels  of  latitude  around 
wMch  each  region  on  the  surface  of  the  earth  is  carried  by 
the  diurnal  rotation  of  the  latter  on  its  axis.  It  will  be  seen 
that  in  the  northern  hemisphere  less  than  half  of  these  are 
illuminated  by  the  sun,  and  in  the  jiouthern  hemisphere 
more  than  half.     This  corresponds  to  our  winter  solstice. 

When  the  earth  reaches  -ff,  its  axis  JVS  is  at  right  an- 
gles to  the  line  drawn  to  the  sun,  so  that  the  latter  shines 
perpendicularly  on  the  equator,  the  plane  of  which  passes 
through  it.     The  diurnal  circles  on  the  earth  are  one  half 


no 


A8TB0N0MT. 


illuminated  and  one  half  in  darkness.     This  position  cor- 
responds to  the  vemal  equinox.  ^  a    *^ 

At  G  the  case  is  exactly  the  reverse  of  that  at  A,  the 
sun  shining  more  on  the  northern  hemisphere  than  on  the 
southern  one.  North  of  the  equator  more  than  half  the 
diurnal  circles  are  in  the  illuminated  hemisphere,  and  south 
of  it  less  Here  then  we  have  winter  in  the  southern  and 
summer  in  the  northern  hemisphere.  The  sun  is  above  a 
region  23i°  north  of  the  equator,  so  that  this  position  cor- 
responds to  our  summer  solstice. 

At  D  the  earth's  axis  is  once  more  at  right  angles  to  a 
line  drawn  to  the  sun.  The  latter  therefore  shines  upon 
the  equator,  and  we  have  the  autumnal  equinox. 

In  whatever  position  we  suppose  the  earth,  the  Une  A  JV, 
continued  indefinitely,  meets  the  celestiad  sphere  at  its 
north  pole,  while  the  middle  or  equatorial  circle  of  the 
earth,  continued  indefinitely  in  every  direction,  marks  out 
the  celestial  equator  in  the  heavens.    At  first  sight  it  might 
seem  that,  owing  to  the  motion  of  the  earth  through  so 
vast  a  circuit,  the  positions  of  the  celestial  pole  ^d  equa- 
tor must  change  in  consequence  of  this  motion.     We  might 
say  that,  in  reaUty ,  the  pole  of  the  earth  describes  a  circle  in 
the  celestial  sphere  of  the  same  size  as  the  earth's  orbit. 
But  this  sphere  being  infinitely  distant,  the  circle  thus  de- 
scribed appears  to  us  as  a  point,  and  thus  the  pole  of  the 
heavens  seems  to  preserve  its  position  among  the  stars 
through  the  whole  course  of  the  year.    Again,  we  may 
suppose  the  equator  to  have  a  slight  annual  motion  among 
the  stars  from  the  same  cause.    But  for  the  same  reason 
this  motion  is  nothing  when  seen  from  the  earth.    On  the 
other  hand,  the  slightest  change  in  the  direotim  of  the 
axis  SIf  wUl  change,  the  apparent  position  of  the  pole 
among  the  stars  by  an  angle  equal  to  that  change  of  direc- 
tion.   We  may  thus  consider  the  position  of  the  celestial 
pole  as  independent  of  the  position  of  the  earth  in  its 
orbit,  and  dependent  entirely  on  the  direction  in  which 
the  axis  of  the  earth  points. 


1 


tic 
of 
ex 
diJ 


ch 

is 

th 

pi 

nc 

th 

to 

be 

la 

ri| 

b( 

cc 

til 

di 

cc 

es 

w 

ni 

tt 

si 
C 

ai 
al 
t< 
tl 
b 
o 


cor- 

thc 
1  the 
:  the 
ionth 
I  and 
jve  a 
1  cor- 

to  a 
upon 

SJV, 
Eit  its 
f  the 
C8  ont 
[night 
igh  so 
equa- 
tnight 
vie  in 
orbit, 
osde- 
>f  the 
I  stars 
e  may 
unong 
reason 
)n  the 
of  the 
o  pole 
direc- 
elestial 
in  its 
which 


CELESTIAL  LATITUDE  AND  LONGITUDE        111 

If  this  axis  were  perpendicular  to  the  plane  of  the  eclip- 
tic, it  is  evident  that  the  sun  would  always  lie  in  the  plane 
of  the  equator,  and  there  would  be  no  change  of  seasons 
except  such  slight  ones  as  might  result  from  the  small 
differences  in  the  distance  of  the  earth  at  different  seasons. 

§  e.    CELESTIAL  LATTTUDB  AND  LONQITUDB. 

Besides  "the  circles  of  reference  described  in  the  first 
chapter,  still  another  systfem  is  used  in  which  the  ecliptic 
is  taken  as  the  fundamental  plane.  Since  the  motion  of 
the  earth  around  the  sun  takes  place,  by  definition,  in  the 
plane  of  the  ecliptic,  and  the  motions  of  the  planets  very 
near  that  plane,  it  is  frequently  more  convenient  to  refer 
the  positions  of  the  planets  to  the  plane  of  the  ecliptic  than 
to  that  of  the  equator.  The  co-ordinates  of  a  heavenly 
body  thus  referred  are  called  its  celestial  Utituds  and 
hmgitude.  To  show  the  relation  of  these  co-ordinates  to 
right  asocmsion  and  declination,  we  give  a  figiwe  showing 
both  co-ordmates  at  the  same  time,  as  marked  on  the 
celestial  sphere.  This  figure  is  supposed  to  be  the  celes- 
tial sphere,  having  the  solar  system  in  its  centre.  The 
direction  />  ^  is  that  of  the  axis  of  the  earth ;  IJ\&  the 
ecliptic,  or  the  great  circle  in  which  the  plane  of  the 
earth's  orbit  intersects  the  celestial  sphere.  The  point  in 
which  these  two  circles  cross  is  marked  0^,  and  is  the  ver- 
nal equinox  from  which  the  right  ascension  and  the  longi- 
tude are  both  counted. 

The  horizontal  and  vertical  circles  show  how  right  ascen- 
sion and  declination  are  counted  in  the  manner  described  in 
Chapter  I.  As  the  right  ascension  is  counted  all  the  way 
around  the  equator  from  (^  to  24S  so  longitude  is  counted 
alon  ,'  the  ecliptic  from  the  point  0^,  or  the  vernal  equinox, 
toward  J  in  degrees.  The  whole  circuit  measuring  360", 
this  dlhtance  will  carry  us  all  the  way  round.  Thus  if  a 
body  ^  in  the  ecUptic,  its  longitude  is  simply  the  number 
o^'i^ees  from  the  vernal  equinox  to  its  position,  meas- 
lllif  !n  the  direction  from  /  toward  J.     If  it  does  not  lie 


1 


112 


A8TR0N0MY. 


SipSo     ffle»gth  of  thi.  i«rpe«dicukr,me«oredm 
^,  i»  cUedX  W«.  of  .ho  IfJy.  f'f  ™y^ 
««^l.  nr  south  whUe  the  distance  of  the  foot  of  the  per 
™^.S^f*m  r  vomal  eqainox  i.  called  '■^^'-f^- 

botoTof  the  Botar  «T»tem,  retatively  to  the  smi,  by  their 
^"X^taat«d«.  lU«.intheecUptiewehave  . 


FlO.  47.— CIBCUCB  OF  THE  BPHBBB. 


plane  more  nearly  fixed  than  that  of  the  equator  On^e 
Ler  hand,  it  is  more  convenient  totepreeent  ^  po«Uon 
of  aU  the  heavenly  bodies  ae  Been  from  the  ««^^y  *^ 
right  ascensions  and  declinations,  because  we  ««»o*  «T; 
rJhriongitudes  and  latitudes  <^%^;\r^f^ 
observe  right  ascension  and  decimation.  If  we  wisn  w 
dSn/the  longitude  and  l^tjude  of  a^y  as  -n 
from  the  centre  of  the  earth,  we  have  to  fi«*/»f ^^«j^^ 
ascension  and  decUnation  by  observation,  and  then  cbm^ 
Sr^nMitities  to  longitude  and  htitude  by  tngonometn- 
oal  formnlsB. 


priB 
nitii 
core 
rate 
ter, 
pki 
the 
uia' 

• 

iut( 
g 
iirsi 
tha 
the 
whi 
mo 
mo 
alw 
cer 
1 
pec 
boc 
sun 
pla 


we 
the 
iin 
^  be 
per- 
ude. 
the 
heir 
vea 


)nthe 
wition 
^  their 
meas- 
riOAly 
rifih  to 
B  seen 
I  right 
shauge 
unetri- 


CHAPTER    IV. 

THE  PLANETARY  MOTIONS. 

§  1.  APPABEnr  Ain>  beal  Monovs  of  the 

FLAITETS. 

DeflnitioiiB. — The  solar  system,  as  wo  now  know  it,  com- 
prises so  vast  a  number  of  bodies  of  various  orders  of  mag- 
nitude and  distance,  and  subjected  to  so  many  seemingly 
complex  motions,  that  we  must  consider  its  parts  sepa- 
rately. Our  attention  will  therefore,  in  the  present  chap- 
ter, be  particularly  directed  to  the  motions  of  the  great 
planets,  which  we  may  consider  as  forming,  in  some  sort, 
the  fundamental  bodies  of  the  system.  These  bodies 
may,  with  respect  to  their  apparent  motions,  be  divided 
into  three  classes. 

Speaking,  for  the  present,  of  the  sun  as  a  planet,  the 
first  class  comprises  the  »un  and  moon.  We  have  seen 
that  if,  upon  a  star  chart,  we  mark  down  the  positions  of 
the  sun  day  by  day,  they  will  all  fall  into  a  regular  circle 
which  marks  out  the  ecliptic.  The  monthly  course  of  the 
moon  is  found  to  be  of  the  same  nature,  although  its 
motion  is  by  no  means  uniform  in  a  month,  yet  it  is 
always  toward  the  east,  and  always  along  or  very  near  a 
certain  great  circle. 

The  second  class  comprises  Venus  and  Mereury.  The 
peculiarity  exhibited  by  the  apparent  motion  of  these 
bodies  is,  that  it  is  an  oscillating  one  on  each  side  «,  ?  the 
sun.  If  we  watch  for  the  appearance  of  one  of  theae 
planets  after  sunset  from  evening  to  evening,  we  shall  find 


i 


ABTR0N0M7. 

it  to  appear  above  the  western  horizon.  Night  after  night 
wiUW arther  and  farther  from  the  sun  untU  it  attems 
ar^Sr  maximum  distance;  then  it^llappearter^^^^ 
to  the  sun  again,  and  for  a  while  to  be  lost  m  its  rays. 
A  f^w  Zs  ISer  it  will  reappear  to  the  west  of  the  ^n, 
fnd  ther^^ter  be  visible  in  the  eastern  horizon  before 
Bunrise  In  the  case  of  Mercury,  the  time  reqmred  for 
oneT»mplete  oscillation  back  and  forth  is  about  four 
Zt?^7and  in  the  case  of  Venus  more  than  a  year  and 

*  m  third  class  comprises  Jfor«,  Jupit^,  and  Saturn  as 
weU  ^a  ^at  num  Jof  planets  not  visible  to  the  na^ed 
Tye      Thfgeneral  or  average  motion  of  these  planets  i 
X'ard  the%  a  complete  revolution  i-    «^«  J^^^^ 
Bphere  being  performed  in  times  ranging  from  two  years 
ZZ  Z^e^Mars  to  164  years  in  that  of  Neptnn.. 
But  instead  of  moving  uniformly  forward,  they^m  to 
have  a  swinging  motion  ;   first,  they  move  forward  or 
towIrJ  Zlt  'through  a  pretty  long  arc  tb-  backw^^ 
or  westward  through  a  short  one,  then  forward  through 
a  J^r  one,  etc.     It  is  only  by  the  excess  of  the  longer 
aiTS  the  shorter  ones  that  the  circuit  of  the  heavens 

^'S'general  motion  of  the  sun,  moon,  and  planets 
among  the  stars  being  tcJward  the  east  the  motion  inth^^ 
diredlon  is  called  direct;  whereas  the  occasional  short 
Z&Z  toward  the  west  are  called  retro^.  During 
the  periods  between  direct  and  retrograde  motion,  the 
pknete  will  for  a  short  time  appear  stationaiy.  ^^^ 

The  planets  Venm  and  Mercury  are  said  to  be  at  great- 
est  ^atUm  when  at  their  greatest  «^"g^;.J«^^^^™ 
the  sun  The  elongation  which  occurs  with  the  planet 
J^tTihe  sun,  andXrefore  visible  in  the  -estei.  hon- 
zon  after  sunset,  is  called  the  eastern  elongation,  the  other 

^T^^irslid  to  be  in  conjunction  with  the  smi  when 
it  is  in  the  same  direction,  or  when,  as  it  seems  to  pass  by 


the  B 
oppo. 
tion- 
apla 
sun, 
yond 
Ai 
knov 
and  \ 
cent! 
plant 
inFi 


in  tl 
whi< 
fari 


/ 


ight 
tains 
itum 
rays. 
Bun, 
afore 
i  for 
four 
r  and 

m  as 

laEked 

lets  is 

lestial 

years 

■kune. 

em  to 

a-d  or 

kward 

rough 

longer 

eavens 

planets 
in  this 
short 
During 
in,  the 

igreat- 
se  from 
planet 
m  hori- 
le  other 

n  when 
pass  by 


ARRANGEMENT  OF  THE  PLANETS. 


116 


the  sun,  it  approaches  nearest  to  it.  It  is  said  to  be  in 
apposition  to  the  sun  when  exactly  in  the  opposite  direc- 
tion— rising  when  the  snn  sets,  and  vi^ie  vecsa.  If,  when 
a  planet  is  in  conjunction,  it  is  between  the  earth  and  the 
sun,  the  conjunction  is  said  to  be  an  inferior  one  ;  if  be- 
yond the  snn,  it  is  said  to  be  tniperior. 

Arrangements  and  Motions  of  the  Planets. — We  now 
know  that  the  sun  is  the  real  centre  of  the  solar  system, 
and  that  the  planets  proper  all  revolve  around  it  as  the 
centre  of  motion.  The  order  of  the  five  innermost  large 
planets,  or  the  relative  positions  of  their  orbits,  are  shown 
in  Fig.  48.     These  orbits  are  all  nearly,  but  not  exactly, 


/ 


48. — ORBIT8  OF  THB  PLANETS. 


in  the  same  plane.  The  planets  JUercury  and  Venits 
which,  as  seen  from  the  earth,  never  appear  to  recede  very 
far  from  the  sun,  are  in  reality  those  which  revolve  inside 


,,„  ASTKONOMr. 

llo 

,  ,  -♦I,  The  Dlanets  of  the  third  clasB, 
the  orbit  of  the  earth.  ?^*  Pn^auces  from  the  «un, 
which  perform  tl^«y^;j-^„^^^^^^^^^  and  ai.;nore 
are  what  we  now  call  the  J^  "*\  t*.  ^f  these,  the  or- 
aietantfj^the^mH^-^^^^  telescopic  planets 

bits  of  Mars,  Jujnter,  ana  a  ^  ^^^ 

are  shown  in  t^>«  ^f  ^^f  ^* Jurvisible  to'^the  naked 
Samr>.,  the  farthest  P^»"«*  ^Ll  telescopic  planets, 
eye,  and  ^^  J^^^;^jteX^l  ^'^^  ^^^^^ 
On  the  scale  of  l?ig.  *»  ^"«  Wnallv,  the  moon  is  a 

^ore  than  two  feet  m  diameter.   ^^Z.U.  ^^^.^e,  and 

The  farther  »?!»««*  i^^*^^^  '^e  go  frJm  tbe  sun, 
is  its  orbital  motion.  TW ^^  f^,  ^he  double  reason 
the  periods  of  revolution  are  ^«J««'^;^**J^ribe  and  moves 
that  the  planet  has  a  larger  orbit    o  de^"^^^.^^  ^^  ^^^ 

xnonj  slowly  in it«  orbit,    f^^^^^^^^^trognide motion 
outerplanetsthattheoccasiomaapp««ntreirog 

li  Jplanets  is  du.  - -y^r<^^W  a  pU, 
We  first  remark  that  the  ^Pl^j^^  ,     ^^  li^e  joining 
as  seen  from  the  «^%»  *^^^t  Z  to  be  continued 
the  earth  and  planet.    S^I^^lt  tbe  celestial  sphere, 
onward  to  infinity,  so  as  to  ^^J^^^^J^J^efined  by  the 
the  apparent  motion  of  t^l^P^''?*  ^^temcte  the  sphere, 
motion  of  the  point  ^^^^^f  ^^^^^^^^^^^       dir^t ;  if 
If  this  motion  is  toward  the  east,  it  wiu  oe 
toward  the  west,  retrograde.  g 

^ V"/^X*JV ':  Cu^clTve  "^Itioi^  of  the  earth 
poee  ^i^^ff^cDEF  ^  ^«  corresponding  posi- 
in  its  orbit,  wAABtVJ;^  Tt  must  be  remembered  that 
tions  of  ^-- -  fXTi^Tnti^cTnnection,  we  do 
irmiraf  alir  dl^ction  in  space,  but  a  direction 


aronr 
down 
diroc 
inovt 
earth 
beini 
evidi 
great 
sun  I 
totl 


^ 

the 
dir 
the 
H 
pel 
inj 
eai 
is 


ItJ 


lird  cla8B, 
i  the  Bun, 

are  jnore 
se,  the  or- 
lic  planets 
Iter  comes 
the  naked 
ic  planets. 
I  would  be 

moon  is  a 
sentro,  and 
an. 
inude  that 

outside  that 

I,  the  Blower 
9m  the  sun, 
)uble  reason 
}  and  moves 
lotion  of  the 
grade  motion 

ring  Fig-  49- 
of  a  planet, 
i  line  joining 
be  continued 
cstial  sphere, 
efined  by  the 
its  the  sphere, 
be  direct ;  if 

pUnet.  Sup- 
riB  of  the  earth 
spending  posi- 
membered  that 
inection,  we  do 
but  a  direction 


APPABBNT  MOTIONS  OF  TlIK  PLANKTS.         117 

around  the  sphere.  In  the  figure  wc  are  supposed  U  <k 
•lown  upon  the  planetary  orbitH  from  the  north,  anu  a 
direction  west  is,  tlien,  that  in  which  the  ImudH  of  a  watch 
move,  while  east  is  in  the  opposite  direction.  When  the 
earth  is  at  //  the  planet  is  seen  at  A.  The  Ime  JIA 
being  supposed  tangent  to  the  orbit  of  the  planet,  it  is 
evident  from  geometrical  considerations  that  this  is  the 
Kreatest  angle  which  the  planet  can  ever  make  with  the 
sun  as  seen  from  the  earth.  This,  therefore,  corresponds 
to  the  greatest  eastern  elongation. 


When  the  earth  has  reached  /the  planet  is  at  B,  and  is 
therefore  near  the  direction  IB.  The  line  has  turned  in  a 
direction  opposite  that  of  the  hands  of  a  watch,  and  cuts 
the  celestial  sphere  at  a  point  farther  east  than  the  line 
ffA  did.  Hence  the  motion  of  the  planet  during  this 
period  has  been  direct ;  but  the  direction  of  the  sun  hav- 
ing changed  also  in  consequence  of  the  advance  of  the 
earth,  the  angular  distance  between  the  sun  and  the  planet 
is  less  than  before. 

While  the  earth  is  passing  from  /  to  K,  the  planet 


118 


ASTRONOHr. 


pasHuH  from  li  to  C.  The  distance  B  C  ox(!«odH  /  A',  be- 
cause the  planet  niovet)  faster  than  the  earth.  The  line 
joining  the  earth  and  planet,  therefore,  cuts  the  celestial 
sphere  at  a  point  farther  west  than  it  did  l)eforo,  and 
therefore  the  direction  of  the  apparent  motion  is  retro- 
grade. At  G  the  planet  is  in  inferior  conjunction.  The 
retrograde  motion  still  continues  imtil  the  earth  reaches  Z, 
and  the  planet  />,  when  it  1>ecomcs  stationary.  After- 
ward it  is  direct  until  the  two  bodies  again  come  into  the 
relative  positions  I  Ji. 

Let  U8  next  snpposo  that  the  inner  orbit  A  B  CD  EF 
represents  that  of  the  earth,  and  the  outer  one  that  of  a 
superior  planet,  Moth  ior  instance.  We  may  consider 
O  QPJitohe  the  celestial  sphere,  only  it  should  be  infi- 
nitely distant.  While  the  earth  is  n  «yving  from  ^  to  ^  the 
planet  moves  from  II  to  7.  This  ^ni.  tion  is  direct,  the  di- 
rection OQP li  being  from  west  to  east.  While  tlie earth 
is  moving  from  B  to  D,  the  planet  Is  moving  from  /  to 
Z ;  the  former  motion  l)eing  the  more  rapid,  the  earth 
now  passes  by  the  planet  as  it  were,  and  the  line  conjoin- 
ing tiiem  turns  in  the  same  direction  as  the  hands  of  a 
watch.  Therefore,  during  this  time  the  planet  seenu*  to 
describe  the  arc  P  Q'  in  the  celestial  sphere  in  the  direction 
opposite  to  its  actuai  orbital  motion.  The  lines  Z  D  and 
MEixe  supposed  to  be  parallel.  The  planet  is  then  really 
stationary,  even  though  as  drawn  it  would  seem  to  have  a 
forward  motion,  owing  to  the  distance  of  these  two  lines, 
yet,  on  the  infinite  sphere,  this  distance  appears  as  a 
point.  From  the  point  M  the  motion  is  direct  until  the 
two  bodies  once  more  reach  the  relative  positions  B  I. 
When  the  planet  is  at  JT  and  the  earth  at  C,  the  former  is 
in  opposition.  Hence  the  retrograde  motion  of  the  supe- 
rior planets  always  takes  place  near  opposition. 

Theory  of  Bpioy<des. — The  ancient  astronomers  repre- 
sented this  oscillating  motion  of  the  planets  in  a  way  which 
was  in  a  certain  sense  correct.  The  only  error  they  made 
was,  in  attributing  the  oscillation  to  a  motion  of  the  planet 


API 

instead  of 

really  cans 

the  nteans 

tion  of  the 

celebrated 

motions  w 

Ulcus.     C 

seen  by  tl 

sented  by 

circle  or « 

with  a  rei 

then  the 

f erence  c 

true  one 

epicycle 

the  sun, 

cumferei 

from  tht 

plain  thi 

motion. 

Itisi 

motion 

pear  to 

which  1 

is  uncoi 

appear 

shown 

and^ 

the  obi 

imagin 

Suppo 

the  pi 

rest,  s 

have 


imagi 
thep 


APPARBNT  MOTIONS  OF  TIIK  PLANKTH. 


119 


1DEF 
at  of  a 
ionsider 
be  infi- 
o  R  the 
the  di. 
le  earth 
m  /to 
e  eartJi 
Jonjoin- 
^ds  of  a 
senifi  to 
irection 
'/>and 
D  really 
have  a 
o  lines, 
rs  as  a 
itil  the 
wJ?/ 
pmer  is 
3  sope- 

repre- 

whioh 

made 

planet 


insteatl  of  a  motion  of  the  earth  around  the  sun,  whiclk 
really  causes  it.  But  their  theory  was,  notwithstanding, 
tlie  means  of  leading  Cupeuniuus  and  others  to  the  percep- 
tion of  the  true  nature  of  the  motion.  We  allude  to  the 
celebrated  theory  of  epicycles,  by  which  the  planetary 
motions  were  always  represented  before  the  time  of  Copkk- 
NiciTB.  Complicated  though  these  motions  were,  it  was 
seen  by  the  ancient  astronomers  that  they  could  be  repre- 
sented by  a  combination  of  two  motions.  First,  a  small 
circle  or  epicycle  was  supposed  to  move  around  the  earth 
with  a  regular,  though  not  uniform,  forward  motion,  and 
then  the  planet  was  supposed  to  move  around  the  oircnm- 
ference  of  this  circle.  The  relation  of  this  theory  to  the 
true  one  was  this.  The  regular  forward  motion  of  the 
epicycle  represents  the  real  motion  of  the  planet  aronnd 
the  sun,  while  the  motion  of  the  planet  aronnd  the  cir- 
cumference of  the  epicycle  is  an  apparent  one  arising 
from  the  revolution  of  the  earth  around  the  snn.  To  ex- 
plain this  we  must  understand  some  of  the  laws  of  relative 
motion. 

It  is  familiarly  known  tl)at  if  an  observer  in  unconscious 
motion  looks  upon  an  object  at  rest,  the  object  will  ap- 
pear to  him  to  move  in  a  direction  opposite  that  in 
which  he  moves.  As  a  result  of  this  law,  if  the  observer 
is  unconsciously  describing  a  circle,  an  object  at  rest  will 
appear  to  him  to  describe  a  circle  of  equaJ  size.  This  is 
shown  by  the  following  figure.  Let  8  represent  the  sun, 
and  A  B  CDBF  the  orbit  of  the  earth.  T^  us  suppose 
the  observer  on  the  earth  carried  around  in  this  orbit,  but 
imagining  himself  at  rest  at  8^  the  centre  of  motion. 
Suppose  he  keeps  observing  the  direction  and  distance  of 
the  planet  P,  which  for  the  present  we  suppose  to  be  at 
rest,  since  it  is  only  the  apparent  motion  that  we  shall, 
have  to  consider.  When  the  observer  is  at  ^  he  really 
sees  the  planet  in  a  direction  and  distuioe  A  P,  but 
imagining  himself  at  8  he  thinks  he  sees  the  planet  at 
the  point  a  determined  by  drawing  a  line  Sa  parallel  and 


120 


ASTHONOMV. 


equal  to  A  P.     A*  he  pam-H  from  A  to  B  the  planet 
will  wjeui  to  him  to  move  in  the  opiKwite  ilirection  fr(»m 

A  to  b,  the  point  h  Injiiig  deter- 
mined by  drawing  Sb  equal  and 
parallel  to  B  P.     As  ho  reeedes 
from  the  planet  through  the  arc 
BCDy  the  planet  seems  to  re- 
cede  from    him   through  hcd\ 
and  while  he  moves  from  loft  to 
right   through   DE  the    planet 
seeniB  to  move  from  right  to  left 
through  D  E.     Finally,  as  he  ap- 
proaches the  planet  through  the 
arc  EFA  the  planet  seems  to 
approach    him    through   EFA, 
and  when  he  returns  to  A  the 
pUnet  will  appear  at  ^,  as  in  the 
beginning.      Thus    the    planet, 
though  really  at  rest,  will  seem 
to  him  to  move  over  the  circle 
ahcdef  corresponding  to   that 
iu  which  the  obser^'er  himself  is 

carried  around  the  sun. 

Tlie  planet  being  really  in  motion,  it  is  evident  that 
the  combined  effect  of  the  real  motion  of  the  planet  and 
the  apparent  motion  around  the  circle  a  J  o  <; «/ will  bo 
represented  by  carrying  the  centre  of  this  circle  P  along 
th.>  true  orbit  of  the  planet.     The  motion  of  the  earth 
being  more  rapid  than  that  of  an  outer  planet,  it  follows 
that  the  apparent  motion  of  the  phmet  through  a  J  is  more 
rapid  than  the  real  motion  of  P  along  the  orbit.    Hence 
in  this  part  of  the  orbit  the  movement  of  the  planet  wUl  be 
retrograde.     In  every  other  part  it  will  be  direct,  because 
the  progressive  motion  of  P  will  at  least  overoome,  some- 
times be  added  to,  the  apparent  motion  around  the  circle. 
In  the  ancient  astronomy  the  apparent  small  circle 
ahcdef  was  called  the  epieyde. 


In 

flm  ri 
I  lero 
ifH  rei 
the  t 
forwt 
tion 
earth 

In 
wo  hi 
by  II 
really 
to  de 
of  iti 
tho  a 
that 
of  itf 
incoi 
all  tl 
was, 
was  1 
mov< 
bratc 
the  I 
of  m 
real 
in  01 
part, 
poset 
Thej 

Tl 
ineqi 
to  b< 

•I 
quity 
Buppc 
idled 


UNEQUAL   MOTION  OF  THE  PLANETS. 


121 


I  planet 
>ii  fr<»iii 
ij  tlotur- 
[ual  iind 

recedos 

the  arc 
8  to  ro- 
ll hed\ 
w  loft  to 
)  planet 
t  to  left 
u  ho  ap- 
)Ug1l  tlio 
iOoinB  to 

EFA, 
o  A  the 
as  in  the 

planet, 
nil  seem 
he  circle 

to  that 
litnBelf  is 

dent  that 
lanot  and 
f  will  bo 
)  P  along 
the  earth 
it  follows 
h  is  more 
.  Hence 
let  will  be 
t,  because 
ne,  some- 
he  circle. 

lall  circle 
t 


In  the  ciiHo  of  \\\v  innor  planets  Mernnnf  and  Vtrnm 
\\w  rbliition  of  tlie  epiiiyelo  to  the  tr.io  orlnt  Ih  reverHed. 
Here  the  epieyelic  motion  ih  tliiit  of  the  plunet  annind 
ifH  real  orbit— that  is,  the  true  orliit  of  the  plunot  around 
tho  sun  was  itself  taken  for  the  epicycle,  while  the 
forward  motion  was  really  duo  to  tho  apparent  revolu- 
tion of  tho  sun  produced  by  tho  aimual  motion  of  tho 
earth. 

In  tho  preceding  descriptions  of  tho  planetary  motions 
wo  have  spoken  of  them  all  as  eircukr.  But  it  was  found 
by  Ilii'J'ARcnus  *  that  none  of  tho  planetary  motions  were 
really  unifonn.  Studying  tho  motion  of  the  sun  in  order 
to  determine  tho  length  of  tho  year,  ho  observed  tho  times 
of  its  passage  through  tho  equinoxes  and  solstices  with  all 
tho  accuracy  which  his  instruments  pennitted.  He  found 
that  it  was  several  days  longer  in  passing  through  one  half 
of  its  course  than  through  tho  other.  This  was  apparently 
incompatible  with  tho  favorite  thcoiy  of  tho  ancients  that 
all  tho  celestial  motions  were  circular  and  uniform.  It 
was,  however,  accounted  for  by  supposing  that  the  earth 
was  not  in  the  centre  6f  tho  circle  around  which  tho  sun 
moved,  but  a  little  to  one  side.  Thus  arose  the  cele- 
brated theory  of  tho  eccentric.  Careful  observations  of 
the  planets  showed  that  they  also  had  similar  inequalities 
of  motion.  The  centre  of  the  epicycle  around  which  the 
real  planet  was  carried  was  found  to  move  more  rapidly 
in  one  part  of  the  orbit,  and  more  slowly  in  the  opposite 
part.  Thus  the  circles  in  which  the  planets  were  sup- 
posed to  move  were  not  truly  centred  upon  the  earth. 
They  were  therefore  called  eccentrics. 

This  theory  accounted  in  a  rough  way  for  the  observed 
inequalities.  It  is  evident  that  if  the  earth  was  supposed 
to  be  displaced  toward  one  side  of  the  orbit  of  the  planet, 

*  HnTAi{CHi7B  was  one  of  thie  most  celebrated  astronomers  of  anti- 
quity, being  frequently  spoken  of  as  the  father  of  the  science.  He  is 
supposed  to  have  made  most  of  his  observations  at  Rhodes,  and  flour- 
hdied  about  one  hundred  and  fifty  years  before  the  Christian  era. 


iiu  Ti 


♦ 


522  ASTRONOMY. 

the  latter  wonkl  seem  to  move  more  rapidly  when  nearest 
the  earth  than  when  farther  fron.  it.     1^  wa.  not  untd  ^e 
time  of  KE..LEK  that  the  eccentric  w;ifl  shown  to  be 
caTable  of  accounting  for  the  real  motion  ;  and  it  ,s  his 
discoveries  which  we  are  next  to  descnbe. 

§  2.    KBPLBB'S  LAWS  OF  PLAJTETARY  MOTION. 

The  direction  of  the  sun,  or  its  longitude,  can  be  deter- 
mined  from  day  to  day  by  direct  observation      If   we 
could  also  observe  its  distance  on  each  day,  we  should,  by 
laying  down  the  distances  and  directions  on  a  large  piece 
7paper,  through  a  whole  year,  be  able  to  trace  the  curve 
Sthe  earth  describes  in  its  annual  course,  this  cour^ 
C^g,  SB  already  shown,  the  counterpart  of  the  appa^^t 
L  of  the  sun.     A  rough  determination  of  *ae  rela- 
tive distances  of  the  sun  at  difierent  times  of  the  year  may 
be  made  by  measuring  the  sun's  apparent  angular  diame- 
ter, becaJe  this  diameter  varies  inversely  aa   Je  distan^ 
of  the  object  observed.     Such  measur^  would  show  that 
the  diameier  waa  at  a  maximum  of  32'  36'  on  January  1st, 
Ind  a"a  minimum  of  31'  32"  on  July  1st  of  every  y«.^ 
The  difference,  64%  is,  in  round  numbers,  A  tbe  mean 
diameter-that  is,  the  earth  is  nearer  the  sun  onjmu^j 
1st  than  on  July  Ist  by  about  ^     We  may  consider  ^ 
as  A  greater  than  the  mean  on  the  one  date,  and  ^  less 
TntheSer.    This  is  therefore  the  actual  displacement 
of  the  sun  from  the  centre  of  the  earth  s  orbit. 

Again,  observations  of  the  apparent  daaly  motion  of 
thT^  among  the  stars,  corresponding  to  the  real  dady 
'IZoi  the'earth  round  the  sun,  show  t^s  motion^o  be  . 
least  about  July  Ist,  when  it  amounts  to  57  12  _  34d^  , 
and  greatest  about   January  1st,  when  it  a^^^^  t° 
«1 '  ir  =  3671'.    The  difference,  239',  is,  m  round  num- 
bers A  the  mean  motion,  so  that  the  range  of  variation 
M;  proportion  to  the  mean,  double  what  it  is  in  the  c^ 
p    L  diBtences.     If  the  actual  velocity  of  the  earth  m  its 


pou] 
was 
pose 


m  01 
in  lo 
half 
long 
eartl 
ingi 
attril 
the  t 
bit- 
centi 
the  ( 
greal 
A] 
tion  : 
radi', 
rouni 
pose, 
and 
day  t 
of  it 
and  I 

geom 
the  a: 
are  ir 


KEPLER'S  Laws. 


Idd 


jarest 
il  the 
ae  iu- 
is  his 


[ON. 

deter- 
[f  wo 
Id,  by 

piece 

curve 
course 
parent 
3  rela- 
armay 
diame- 
istance 
»w  that 
ary  iBt, 

y  y«ar. 

Q  mean 
fanuary 
sider  it 
L^less 
icement 

)tion  of 
al  daily 
on  to  be  ^ 
=  3432', 
rants  to 
nd  num- 
variation 
the  case 
rth  in  its 


orbit  were  niiiforin,  tlie  apparent  angular  motion  round 
tlie  sun  would  be  inversely  as  its  distance  from  the  sun. 
Actually,  however,  the  angidar  motion,  as  given  above,  is 
inversely  as  the  square  of  the  distance  from  the  sun,  be- 
cause (1  +  ^V)'  =  1  +  tV  very  nearly.  The  actual  ve- 
locity of  the  earth  is  therefore  greater  the  nearer  it  is  to 
the  sun. 

On  the  ancient  theory  of  the  eccentric  circle,  as  pro- 
pounded by  IIippAKcnus,  the  actual  motion  of  the  earth 
was  supposed  to  be  uniform,  and  it  was  necessary  to  sup- 
pose the  displacement  of  the  sun  (or,  on  the  ancient  theo- 
ry, of  the  earth)  from  the  "ontre  to  be  ^  its  mean  distance, 
in  order  to  account  for  the  observed  changes  in  the  motion 
in  longitude.  We  now  know  that,  in  round  numbers,  one 
half  the  inequality  of  the  apparent  motion  of  the  sun  in 
longitude  arises  from  the  variations  in  the  distance  of  the 
earth  from  it,  and  one  half  from  the  earth's  actually  mov- 
ing with  a  greater  velocity  as  it  comes  nearer  the  sun.  By 
attributing  the  whole  inequality  to  a  variation  of  distance, 
the  ancient  astronomers  made  the  eccentricity  of  the  or- 
bit—that is,  the  distance  of  the  sun  from  the  geometrical 
centre  of  the  orbit  (or,  as  they  supposed,  the  distance  of 
the  earth  from  the  centi-e  of  the  sun's  orbit) — twice  as 
great  as  it  really  was. 

An  immediate  consequence  of  these  facts  of  observa- 
tion is  Kepleb's  second  law  of  planetary  motion,  that  the 
radii  vectored  drawn  from  the  sun  to  a  planet  revolving 
round  it,  sweep  over  equal  areas  in  equal  times.  Sup- 
pose, in  Fig.  51,  that  /.S' represents  the  position  of  the  sun, 
and  that  the  earth,  or  a  planet,  in  a  unit  of  time,  say  a 
day  or  a  week,  moves  from  P,  to  P,.  At  another  part 
of  its  orbit  it  moves  from  P  to  P,  in  the  same  time, 
and  at  a  third  part  from  P.  to  P..  Then  the  areas 
SP,P,,  SPP„  SP,P,  will  all  be  equal.  A  Kttle 
geometrical  consideration  will,  in  fact,  make  it  clear  that 
the  areas  of  the  triangles  are  equal  when  the  angles  at  S 
are  inversely  as  the  square  of  the  radii  vectores,  SP,  etc., 


*^- 


1^4 


ASTBONOMT. 

.„ee  t„e  exprcion  ,.  the  -  "V^^™^'"  '"  *"  *"° 
angle  at  S  w  very  anaU  «  J  angle  *  X  ^  J 


O    pi   * 


Fig.  51.— law  of  areas. 

1„  the  ttoe  of  K...«  *->  ™-™J*.Cr^^ctd! 

.un'B  '»P'l»%*'r''''r  J™£'3>  S  the  earth  around 
ing  method  of  deternnmng  the  l«ttt  o  ^^  ^^^ 

thl  »m  could  7'\''»^:^;tol^edhyTTOHoBKi■>.^ 
motions  of  the  planet  ^ar.,^*^  ^^^  ^    , 

that  Keplee  was  led  to  his  ceieore  j^  ^ 

motion.    He  found  that "»  P^^^J";^^  „p^«>nt  the 

,r^y  elreular  orb^ho«-7C*^  ejeu^tions  and 

„h<«rvat.ons.  Jf^' ;™f  ™  t  numher  of  hypothes^ 
the  triil  aud  rejection  ot  a  p«  ^^^  ^^^^^ 

he  was  led  to  the  eondusion  .«'»' ««  ^^  j^  the  analo- 
toanelU^.  having  *e™-^^Jtl^;  attthe  planets, 
gieaof  nature  led  *»*«  ™'°"°r„  „f  the  same  chM, 
L  earth  i»«<^V "'°'^„  twX  ™  led  to  enunciate 

S*C^- "^  -"^"  ^"^""^  "'°"°- 

,hich  were  as  follow:  ,^  ^  „  „  .  .^. „..,  Ok, 

^  7ve  the  area  mentioned  above. 


1 


KEPLER' 8  LAWS. 


195 


1 


I.  Eachplanet  moves  around  the  sun  in  an  ellipse,  hav- 
ing the  sun  in  one  of  its  fad. 

II.  The  radius  vector  joining  each  planet  toith  the 
sun,  moves  over  equal  areas  in  equal  times. 

To  these  be  afterward  added  another  showing  the  rela- 
tion between  the  times  of  revolution  of  the  separate 
planets. 

III.  The  square  of  the  tim^  of  revolution  of  each 
planet  is  proportional  to  the  cube  of  its  mean  distance 
from,  the  sun. 

These  three  laws  comprise  a  complete  theory  of  plan- 
etary motion,  so  far  as  the  main  features  of  the  motion  are 
concerned.  There  are,  indeed,  small  vai-iations  from 
these  laws  of  Keplkh,  but  the  laws  are  so  nearly  correct 
that  they  are  always  cmijloyed  by  astronomers  as  the  basis 
of  their  theorios. 

Mathematioal  Theory  of  the  Elliptio  Motion. —  The 
laws  of  Kkpleb  lead  to  problems  of  such  mathematical 
elegance  that  we  give  a  brief  synopsis  of  the  most  impor- 
tant elements  of  the  theory.  A  knowledge  of  the  ele- 
ments of  analytic  geoUietry  is  necessary  to  understand  it. 

Let  us  put : 

a,  the  semi-major  axis  of  the  ellipse  in  which  the  pUuut  moTflt. 
In  the  figure,  if  (7  is  the  centre  of  the  el- 
lipse, and  <9  the  focus  in  which  the  sun  is 
situated,  then <i  =  A  0=  On. 

08 
e,  the  eccentricity  of  the  ellipse  =  — . 

IT,  the  longitude  of  the  perihelion,-  rep> 
resented  by  the  angle  n  8E,  B  being  the 
direction  of  the  vernal  equinox  from 
which  longitudes  are  counted. 

n,  the  mean  angular  motion  of  the 
planet  round  the  sun  in  a  unit  of  time. 
The  actual  motion  being  variable,  the 
mean  motion  is  found  by  dividing  the  As.  01. 

circumference  =  860°  by  the  time  of  revolution. 

T,  the  time  of  revolution. 

Tj  the  distance  of  the  planet  from  the  sun,  or  its  radius  vector,  a 
variable  quantity. 

I.  The  first  remark  we  have  to  make  is  that  the  Mij^ieiUu  of  the 


126  ASTIiONOMY. 

the  ellipse  we  have  : 

8B  =  Bemi-major  axis  =  a,  

BC=  semi  minor  axis  =  a  V 1  —  «', 
or   5  0  =  a  (1  -  i  «')  nearly,  when  e  is  very  small. 

very  nearly,  so  that  flattening  of  the  orbit  is  only  about  ^  or  .02 
of  the  major  axis.  ,  j^      j     ^jjid^  ^  =  .093  ; 

B^t""! -loirs  tff'i«tE.^»l"«  of  tl,,  orbit  U  only 

a  ,cry  cioso  approxnmtion  to  the  true  lorm  o.^     I  '         ^, 

It  1.  Jnl,  leceuar,  to  »"PP°?°  *?  ""°jrof  tl  •  Scentricit,  loto 
re?Sto'o?rS.'rS.?er»S?"™„pre«„t«ioo  o.  the 

-t'  •^,C.X£°o<'t!!iVS:ot  .™m  «io  .-  " 
and  the  greatest  distance  is 

Kefleb  :  Q 

vector  during  such  unit      ^i^"  *^*  J^rfg  ggcond  law.    Therefore, 

jj»"!'^fi5tcto;?r.t:^'ri'?s%hoh,  .r»  oj^th. 

dh^  which  i.  .  »•  V  T^-?..    The  time  re,m»a  to  do  th«i  1» 

.  1»  ll,i.  formula  ,  n,pr»env.  Iho  r«io  of  the  ciroumfereoee  of  the 
circle  to  its  diameter. 


mg 
alB( 


an 


KEPLER'S  LA  WS. 


1»7 


ing  called  T,  the  area  swept  over  with  the  areolar  velocity  4CU 
t\ao\GT.    Therefore 

J  C  2'  =  IT  a'  ^\  —  e' ; 

2irfl*Vf  —  e» 
0  = j5 

The  .luantity  2  t  hero  represents  860%  or  the  whole  circumference, 

called  M.     Therefore 

2ir 

and  , -. 

C  =  a*n  Vl  -  e\ 

This  value  of  0  being  substituted  in  the  expression  for  8,  wc  have 

a'  rt  Vl -"?    *^ 

^= is 

IV     By  Kepleh's  third  law  r  is  proportioned  to  a" ;  that  is, 
IL  is  a  constant  for  all  the  planets.    The  numerical  value  of  this 

and  a  for  the  earth  will  both  be  unity,  and  the  ratio  ^  will    there- 
fore be  unity  for  all  the  planets.    Therefore 
a»  =  2" ;  o  =  r*. 

i^vc^r  ATS-trhricrrormined  with  very  great  pre- 
"^V  °To  find  the  position  of  a  planet  we  must  kno^^t^e  epoch  at 
M^  Wn^irolllfte^^^^^^ 

Se';s;s^he%a£/Thi^^^^ 

^Ssltiorof  the  planet  at  this  time  wc  shall  have 


Area  of  sector  PSk  _  _r 
]\fcaof ^hoie  ellipse       T 


(1). 


128 


ASTRONOMY. 


The  times  r  and  T  being  both  given,  the  problem  is  "^uced  to 
t.  Jt  of  c^tUng  a  given  area  of  the  ellipse  by  a  line  drawn  from  the 
V^„«  to  some  point  of  its  circumference  to  be  found.  This  is 
ISn  as  Slkk'8  problem,  and  may  be  solved  by  analytic  geom- 


TiO.  68. 


the  ratio  of  i>  P  to  D  i*,  or  of  «  to  b.     Hence, 

Area  GPB  :  area  OP'S  =  b:a. 

n  *  «,««  nvn-  ftnffle  P"  0  B  x  i  a»,  taking  the  unit  radius 
as?Se  unU  of'^fgulaJ^lllsfre!'  Hence,  putting  «  for  the  angle 
pf  G  Bvre  have 


Area  CPB  =  -  area  CP* 5  =  J « S  « 
a 


(2). 


Again,  theareaof  the  trianglcOPSisequaltoibaseC^f   x   al- 
titudePD.     AlsoPD  =  ^-P'AandP'i>=  CP' sin  «  =  «sm«. 


Wherefore, 


tri) 


an( 


It  ( 


or, 


PD  =  &sin 


(8). 


KSPLBR'8  LAWS. 


1S9 


By  the  first  principles  of  conic  sections,  C  8,  the  base  of  the 
triangle,  is  equal  to  a  «.     Hence 

Area  CP8  =  iabeMau, 

and,  from  (3)  and  (8), 

Area  SPB  =  Jo  ft  («  —  «Bin  «). 

Substituting  in  equation  (1)  tliis  value  of  the  sector  area,  and 
IT  a  6  for  the  area  of  the  ellipse,  we  have 

tt  —  g  sin  w  _  jr 
3^;^       ~  2" 


or. 


u  —  «  sin  u  =  2  T  -^. 


Prom  this  equation  the  unknown  angle  «  «  ^^*^^:V'^ 
equation  being*a  transcendental  one,  this  ««"»"«»  ^,^°°«f^"?L 
but  it  may  be  rapidly  done  by  successive  approximation,  or  the 
value  of  u  may  be  developed  in  an  infinite  series. 

Next  we  wi^h  to  expreiTthepositionof  *£«  P»"'«*i.^J^^Si?,K 
by  its  radius  vector -8  P  and  the  angle  B  8  ^,^,^|«f  *7"^'^''" 
vMtor  makes  with  the  major  axis  of  the  orbit.    Let  us  put 

r,  the  radius  vector  SP, 

/'  the  angle  B  3P,  called  the  true  anomaly. 

Then  .     „^ 

r  sin/  =  P2>  =  ft  sin  «  (Equation  8), 

rcos/=8D=CD-  08=  0  P  cosu  -  ae  =  a(coiu-e), 

from  which  r  and  r  can  both  be  determined.  By  taking  the  square 
I^^oTtiS^sums  ohhe  squares,  they  give,  by  suUable  reducbon  and 
putting  ft'  =  a'  (1  -  «'), 

r  =  a  (1  —  «  cos  u), 
and,  by  dividing  the  first  by  the  second, 

ft  sin  « 


tan/  = 


a  (cos  M  —  «) 


Vl  —  g'  sin  M 
cos u-  e 


Prtttog,  „  before,  .  for  the  longtad.  of  th.  peritaUon,  th.tr.. 

'°t'°T;s'.X''^woVS°rpT::iKuti;..,.o  th.  ..upuc, 


180 


ASTRONOMY. 


the  inclination  of  the  orbit  to  the  ecliptic  has  to  be  taken  into  ac- 
counf  The  orbits  of  the  several  large  planets  do  not  lie  in  the 
Smc  plane,  but  are  inclined  to  each  other,  and  to  the  ecliptic,  by 
tft^ous  imkll  anirles.  A  table  giving  the  values  of  these  angles 
;rb"e  g™en  her&r,  from  whi?h  it^ill  be  seen  that  the  orbu  o 
Mereurv^haA  the  greatest  inclination,  amounting  to  7  ,  and  that  of 
f/mSe  least,  teing  only  40'.  The  reduction  of  the  position  of 
tlHw  to  «;«  ecliptic  fs  a  problem  of  spherical  trigonometry, 
the  solution  of  which  need  not  be  discussed  here. 


1 

fun 

whi 

feal 

rea< 

trat 

fiho 

cov 

teBl 

abi 

of 

Ion 

tig 

iB< 

foi 

Bci 


i'- 1 


gr( 
th( 
tb 
ex 
tis 

& 
in 


nto  ac- 
)  in  the 
jtic,  by 
angles 
orbit  of 
that  of 
ition  of 
ometry, 


CHAPTER   V. 

UNIVERSAL  GRAVITATION. 
§  1.    NEWTON'S  LAWS  OP  MOTION. 

The  eBtablishment  of  the  theory  of  universal  gravitation 
furnishes  one  of  the  best  examples  of  scientific  method 
which  is  to  be  found.    We  shall  describe  its  leadmg 
features,  less  for  the  purpose  of  making  known  to  the 
reader  the  technical  nature  of  the  process  than  for  illus- 
trating the  true  theory  of  scientific  investigation,  and 
Bhowing  that  such  investigation  has  for  its  object  the  dis- 
covery of  what  we  may  call  generalized  facts.     The  real 
test  of   progress  is  found  in  our  constantly  increased 
abiUty  to  foresee  either  the  course  of  nature  or  the  eSects 
of  any  accidental  or  artificial  combination  of  causes.    So 
long  as  prediction  is  not  possible,  the  desires  of  the  mves- 
tiinTtor  remain  unsatisfied.    When  certainty  of  prediction 
is  once  attained,  and  the  laws  on  which  the  prediction  is 
founded  are  stated  in  their  simplest  form,  the  work  of 
science  is  complete.  ,  . 

The  whole  process  of  scientific  generalization  consists  in 
grouping  facts,  new  and  old,  under  such  general  laws  that 
they  are  seen  to  be  the  result  of  those  laws,  combined  with 
those  relations  in  space  and  time  which  we  may  suppose  to 
exist  among  the  material  objects  investigated  It  ib  essen- 
tial  to  such  generalization  that  a  single  law  shall  suffice  for 
grouping  and  predicting  several  distinct  facts.  A  law 
invented  simply  to  account  for  an  isolated  fact,  however 


17 


'.'If' 


II 


Wi 


ASTBONOMY. 


general,  cannot  be  regarded  in  gcienco  as  n  law  of  nature. 
It  may,  indued,  bo  true,  Imt  its  truth  caniiut  lie  proved 
until  it  is  shown  that  eeverol  distinct  facts  can  he  accounted 
for  by  it  better  than  by  any  other  law.  The  reader  will 
call  to  mind  the  old  fable  which  represented  the  earth  as 
suppoi'ted  on  the  back  of  a  tortoise,  but  totally  forgot  that 
the  support  of  the  tortoise  needed  to  be  accounted  for  as 
much  as  that  of  the  earth. 

To  tlie  pre-Newtonian  astronomers,  the  phenomena  of  the 
geometrical  laws  of  planetary  motion,  which  we  have  just 
described,  formed  a  group  of  facts  having  no  connection 
with  any  thing  on  the  earth.  Tlie  epicycles  of  Hippakciiits 
and  Ptolkmv  were  u  truly  scientilic  conception,  in  that  they 
explained  the  seemingly  erratic  motions  of  the  planets  by 
a  single  simple  law.  In  the  heliocentric  theory  of  Coper- 
MiODS  this  law  was  still  further  simplified  by  dispensing  in 
great  part  with  the  epicycle,  and  replacing  the  latter  by  a 
motion  of  tho  earth  around  the  sun,  of  the  same  nature 
with  the  motions  of  the  planets.  But  Copebnicds  had  no 
way  of  accounting  for,  or  even  of  describing  with  rigor- 
ous accuracy,  the  small  deviations  in  the  motions  of  the 
planets  around  the  sun.  In  this  respect  he  made  no  real 
advance  upon  the  ideas  of  the  ancients. 

Kepleb,  in  his  discoveries,  made  a  great  advance 
in  representing  the  motions  of  all  the  planets  by  a 
single  set  of  simple  and  easily  understood  geometrical 
laws.  Had  the  planets  followed  his  laws  exactly,  the 
theory  of  planetary  motion  would  have  been  substiuitially 
complete.  Still,  further  progress  was  desired  for  two 
reasons.  In  the  first  place,  the  laws  of  Keplkr  did  not 
perfectly  represent  all  the  planetary  motions.  When  ob- 
servations of  the  greatest  accuracy  were  made,  it  was  found 
that  the  planets  deviated  by  small  amounts  from  the  ellipse 
of  Kepler.  Some  small  emendations  to  the  motions  com- 
puted on  the  elliptic  theory  were  therefore  necessary. 
Had  this  requirement  been  fulfilled,  still  another  step 
would  have  been  desirable — namely,  that  of  connecting  the 


8 

t 

n 
c 
1 

tl 
1 

V 
Ci 

1« 
f< 

it 
f« 
n 
tl 

i 

t 
t 
ii 
I 


^ 


LAWS  OF  MOTION. 


188 


turo. 
oved 
intc<l 
•will 

til  U8 

;  that 
ior  as 

jfthe 

5  just 

jctiou 

KCII178 

ttboy 
Bts  by 

loPKB- 

ing  in 
r  by  a 
nature 
lad  no 
rigor- 
of  the 
10  real 

ivance 
by  a 
letrical 
ly,  the 
mtially 
or  two 
did  not 
ben  ob- 
£  found 
s  ellipse 
as  com- 
cessary. 
ler  step 
ting  the 


motions  of  the  planets  with  motion  upon  the  earth,  and 
reducing  them  to  the  same  laws. 

Notwithstanding  the  great  step  which  Kepi/kr  made  in 
describing  the  celestial  motions,  ho  unveiled  none  of  the 
great  mystery  in  which  they  were  enshrouded.    This  mys- 
tery was  then,  to  all  appearance,  impenetrable,  becaiwc 
not  the  slightest  likeness  could  be  perceived  between  the 
celestial  motions  and  motions  on  the  surface  of  the  earth. 
The  difficulty  was  recognized  by  the  older  philosophers  in 
the  division  of  motions  into  "  forced  "  and  "  natural. 
The  latter,  they  conceived,  went  on  perpetually  from  the 
very  nature  of  things,  while  the  former  always  tended  to 
cease.     So  when  Kepler  said  that  observation  showed  tfej> 
law  of  planetary  motion  to  be  that  around  the  circum- 
ference of  an  ellipse,  as  asserted  in  his  law,  he  said  all  that 
it  seemed  possible  to  learn,  supposing  the  statement  per- 
fectly exact.    And  it  was  all  that  could  he  learned  from  the 
mere  study  of  the  planetary  motions.     In  order  to  connect 
these  motions  with  those  on  the  earth,  the  next  step  wm  to 
study  the  laws  of  force  and  motion  here  around  us.     Sm- 
gukr  though  it  may  appear,  the  ideas  of  the  ancients  on 
this  subject  were  far  more  erroneous  than  then-  concep- 
tions of  the  motions  of  the  planets.     We  might  ahnost  say 
that  before  the  time  of  Galileo  scarcely  a  single  correct 
idea  of  the  laws  of  motion  was  generally  entertained  by 
men  of  learning.     There  were,  indeed,  one  or  two  who  in 
this  respect  were  far  ahead  of  their  age.     Leonardo  da 
Vinci,  the  celebrated  painter,  was  noted  in  this  respect. 
But  the  correct  ideas  entertained  by  him  did  not  seem  to 
make  any  headway  in  the  world  until  the  early  part  of 
the  seventeenth  century.     Among  those  who,  before  the 
time  of  Newton,  prepared  the  way  for  the  theory  in 
question,  Galileo,  Hutghbns,  and  Hooke  are  entitled  to 
especial  mention.     As,  however,  we  cannot  develop  the 
history  of  this  subject,  we  must  pass  at  once  to  the  gen- 
eral laws  of  motion  Ldd  down  by  Newton.     These  were 
three  in  number. 


184 


A8TR0N0M7. 


Law  First :  Jl^jery  body  preserves  its  stats  qf  rest  or  (ff 
un'tform  motion  in  a  right  Htm,  tnUens  it  is  compelled  to 
change  that  state  by  forces  impressed  thereon. 

It  waft  foimorly  eiipposcd  that  a  XwAy  acted  on  by  no 
forco  tended  to  come  to  rest.  Here  lay  one  of  the  great- 
est difflcultioB  which  the  predecessors  of  Newton  found, 
in  accounting  for  tlie  motion  of  the  planets.  The  idea 
that  the  sun  in  some  way  caused  these  motions  was  enter- 
tained from  the  earliest  times.  Even  I*T0LBMr  had  a 
vague  idea  of  a  forco  which  was  always  directed  toward 
the  centre  of  the  earth,  or,  which  was  to  him  the  same 
thing,  toward  the  centre  of  the  universe,  and  which  not 
.only  caused  heavy  bodies  to  fall,  bat  bound  the  whole  nni- 
versfl  together.  Kepleb,  again,  distinctly  aifiims  the  ex- 
istence of  a  gravitating  force  by  which  the  sun  acts  on  the 
planets  ;  but  he  supposed  that  the  sun  nmst  also  exercise 
an  impulsive  forward  force  to  keep  the  planets  in  motion. 
The  reason  of  this  incorrect  idea  was,  of  course,  that  all 
bodies  in  motion  on  the  surface  of  the  earth  had  practically 
come  to  rest.  But  what  was  not  clearly  seen  before  the 
time  of  Kewton,  or  at  least  before  Gald^eo,  was,  that  this 
arose  from  the  inevitable  resisting  forces  which  act  upon 
all  moving  bodies  around  us. 

Law  Second  :  The  aU&raUon  of  motion  is  ewr  propor- 
tional to  ike  mooing  force  impressed,  and  is  made  in  the 
direction  qf  the  right  line  in  which  that  force  acts. 

The  first  law  might  be  conddered  as  a  particular  case  of 
this  second  one  arising  when  the  force  is  supposed  to  van- 
ish. The  accuracy  of  both  laws  can  be  proved  only  by 
very  carefully  conducted  experiments.  They  are  now 
considered  as  mathematically  proved. 

Law  Third :  Toevery  action  there  isahoays  qfy)08ed  an 
equal  reaction  /  or  the  mtitual  actions  of  two  bodies  "wpon 
each  other  are  always  equal,  and  in  opposite  directions. 

That  is,  if  a  body  A  acts  in  any  way  upon  a  body  B, 
B  will  exert  a  force  exactly  equal  on  ^  in  the  opposite 
direction. 


lat 

tlu 

to 

mo 

of 

la/u 

am 

OR] 

seal 
con 
obv 
cull 
in  a 
peri 
fort 
ive 

circ! 

law 

fOH 

low 
cen 
bits 
sun 
mol 
the 


witl 
will 


rest  or  cf 
TmpeUed  to 

I  on  by  no 
'  the  j^roat- 
rTON  found, 
The  idea 
J  was  ontor- 
KMY  liad  a 
jted  toward 
n  the  same 
I  which  not 
a  whole  nni- 
litns  the  ox- 
I  acts  on  the 
ilso  exercise 
B  in  motion, 
irso,  that  all 
d  practically 
1  before  the 
iras,  that  this 
ich  act  upon 

everjtropor- 
made  in  the 
e  acts. 

icular  case  of 
posed  to  van- 
oved  only  by 
'hey  are  now 

</8  opposed  cm, 
0  bodies  tipon 
e  directions, 
m  a  body  B, 
the  opposite 


OliA  VITATION  OF  TUK  PLANKT8. 


180 


These  laws  onco  established,  it  l>ocame  possible  to  calcu- 
late the  motion  of  any  body  or  system  of  bodies  when  oncu 
the  forces  which  act  on  them  wore  known,  and,  vice  versa, 
to  define  what  forces  were  re<^uisite  to  produce  any  given 
motion.  The  question  which  presented  ifaself  to  the  mind 
of  Newton  and  his  contemporaries  was  this  :  Under  what 
lo^  (if force  will  planets  move  round  the  sun  in  accord- 
ance with  Kepi.kr'b  laws  t 

The  laws  of  central  forces  had  been  discovered  by  IIuy- 
OHENS  some  time  before  Newton  commenced  his  re- 
searches, aad  there  was  one  result  of  them  which,  taken  in 
connection  with  Kbpleb'b  third  law  of  motion,  was  so 
obvious  that  no  mathematician  could  have  had  much  diffi- 
culty in  perceiving  it.  Supposing  a  body  to  move  around 
in  a  circle,  and  putting  R  the  radius  of  the  circle,  T  the 
period  of  revolution,  IIuyoiiens  showed  that  the  centrifugal 
force  of  the  body,  or,  which  is  the  same  thing,  the  attract- 
ive force  toward  the  centre  which  would  keep  it  in  the 

circle,  was  proportional  to  ^.    But  by  Kepler's  third 

law  7"  is  proportional  to  I^.    Therefore  this  centripetal 

R  1 

force  is  proportional  to  -^j,  that  is,  to  -^.  Thus  it  fol- 
lowed immediately  from  Kepler's  third  law,  that  the 
central  force  which  would  keep  the  planets  in  their  or- 
bits was  inversely  as  the  square  of  the  distance  from  the 
sun,  supposing  each  orbit  to  be  circular.  The  first  law  of 
motion  once  completely  understood,  it  was  evident  that 
the  planet  needed  no  force  impelling  it  forward  to  keep 
up  its  motion,  but  that,  once  started,  it  would  keep  on 
forever. 

The  next  step  was  to  solve  the  problem,  what  law  of 
force  will  make  a  planet  describe  an  ellipse  around  the 
sun,  having  the  latter  in  one  of  its  foci  ?  Or,  supposing 
a  planet  to  move  rotmd  the  sun,  the  latter  attracting  it 
with  a  force  inversely  as  the  square  of  the  distance  ;  what 
will  be  the  form  of  the  orbit  of  the  planet  if  it  is  not  cir- 


is. 


■4 — '- 


136  AamONOMT. 

cnlar  ?  A  solution  of  cither  of  these  problems  was  beyond 
ArpowetoTmathematicians  before  the  time  o  Newton  ; 
Ind^ttaremained  uncertain  whether  the  planets  uh>v- 
wlder  the  influence  of  the  sun's  gravxtation  would  or 
wouW  not  describe  elUpses.  Unable  at  first,  to  reach  a 
raJSLtory  solution,  Newton  attacked  the  problem  m 

:Sw  Section,  sUng  f-\*^«  n-^n^ll^tinl 
the  sun,  but  of  the  earth,  as  explained  m  the  following 

section. 

§  2.    OBAVTPATION  IN  THE  HEAVENS. 

The  reader  is  probably  familiar  with  the  story  of  N  ew- 
J^  and  the  falling  apple.     Although  it  has  «o  authonta- 
TeToundation,  if  is  strikingly  illustrative  of  the  method 
by  wWch  New;,k  first  reached  a  solution  of  the  problem. 
fi,e  course  of  reasoning  by  which  he  ascended  from  gra^v- 
itetion  on  the  earth  to  the  celestial  motions  was  as  f^^ . 
We  see  that  there  is  a  force  acting  all  over  the  earth  by 
which  all  bodies  are  drawn  toward  its  centre     This  force 
S  f^ar  to  every  one  from  his  infancy,  and  is  property 
^ed  gravitation.    It  extends  without  sensible  diminut^n 
TtheTops  not  only  of  the  highest  braidings,  but  of  the 
highest  mountains.    How  much  higher  does  it  extend? 
my  should  it  not  extend  to  the  moon  ?    If  it  does,  the 
moon  would  tend  to  drop  toward  the  earth,  ]ust  as  a  stone 
^Zvm  from  the  hand  drops.    As  the  moon  moves  romid 
Sr^th  in  her  monthly  cou«e,  there  -ust  be  some  ^rce 
drawing  her  toward  the  earth ;  else,  by  the  first  law  of 
motionfshe  wouldflyentirely  away  in  a  straight  hue.  Why 
Zuld  not  the  force  which  makes  the  apple  fall  be  the 
^ioL  which  keeps  her  in  her  orbit  ?    To  answer  tlus 
^^ion,itwasnotonTynece8sarytocalcuktethemten«ty 

of  the  firce  which  would  keep  the  moon  herself  in  her 
orbit  but  to  compare  it  with  the  intensity  of  gravity  at  the 
S's  surface.  &  long  been  know,  that  ^e  distanc^^ 
of  the  moon  was  about  sixty  radu  of  the  earth.    If  this 


for© 
then 
the  I 
teen 
were 

The 


GliA  VITATION  OF  THE  PLANETS. 


137 


5yond 

fTON  ; 

mov- 
ald  or 
aach  a 
>in  in 
aot  of 
owing 


:  New- 

horita- 

nethod 

oblem. 

a  grav- 

jllows : 

arthby 

is  force 

•roperly 

linution 

of  the 
extend  ? 
oes,  the 

a  stone 
» round 
ne  force 
;  law  of 
a.  Why 
I  be  the 
iwer  this 
intensity 
f  in  her 
ty  at  the 

distance 

If  this 


force  diminished  as  the  inverse  square  of  the  distance, 
then,  at  the  moon,  it  would  be  only  ^^  as  great  as  at 
the  surface  of  the  earth.     On  the  earth  a  body  falls  six- 
teen feet  in  a  second.     If,  then,  the  theory  of  gravitation 
were  correct,  the  moon  ought  to  fall  toward  the  earth 
^^-^  of  this  amount,  or  about  ^  of  en  inch  in  a  second. 
The  moon  being  in  motion,  if  we  imagine  it  moving  ui  a 
straight  line  at  the  beginning  of  any  second,  it  ought  to 
be  drawn  away  from  that  Une  -^  of  an  inch  at  the  end  of 
the  second.     When  the  calculation  was  made  with  the 
correct  distance  of  the  moon,  it  was  found  to  agree  ex- 
actly with  this  result  of  theory.     Thus  it  was  shown  that 
the  force  which  holds  the  moon  in  lier  orbit  is  the  same 
which  makes  the  stone  fall,  only  diminished  as  the  inverse 
square  of  the  distance  from  the  centre  of  the  earth.* 

As  it  appeared  that  the  central  forces,  both  toward  the 
sun  and  toward  the  earth,  varied  inversely  as  the  squares 
of  the  distances,  Newton  proceeded  to  attack  the  mathe- 
matical problems  involved  in  a  more  systematic  way  than 
any  of  his  predecessors  had  done.  Kepler's  second  law 
showed  that  the  line  drawn  from  the  planet  to  the  sun 
will  describe  equal  areas  in  equal  times.  Newton  showed 
that  this  could  not  be  true,  imless  the  force  which  held 
the  planet  was  directed  toward  the  sun.  We  have  already 
stated  that  the  third  law  showed  that  the  force  was  in- 
versely as  the  square  of  the  distance,  and  thus  agreed  ex- 
actly with  the  theory  of  gravitation.     It  only  remained  to 

*  It  is  a  remarkable  fact  in  the  history  of  science  that  Newton 
would  have  reached  this  result  twenty  yec\rs  sooner  than  he  did,  had 
he  not  been  misled  by  adopting  an  erroneous  v  alue  of  the  earth's  diame- 
ter. His  first  attempt  to  compute  the  earth's  gravitation  at  the  distance 
of  the  moon  was  made  in  1665,  when  he  was  only  twenty-three  year«  of 
age.  At  that  time  he  supposed  that  a  degree  on  the  earth's  surface  was 
sixty  statute  miles,  and  was  in  consequence  led  to  erroneous  results  by 
supposing  the  earth  to  be  smaller  and  the  moon  nearer  than  they  really 
were.  He  therefore  did  not  make  public  his  ideas  ;  but  twenty  years 
later  he  learned  from  the  measures  of  Picabd  in  Prance  what  the  true 
diameter  of  the  earth  was,  when  he  repeated  his  calculation  with 
entire  success. 


tiC-S'jBfW" 


paMP 


ir 


I: 
I 

i!; 


138 


ASTRONOMY. 


consider  the  results  of  the  first  law,  that  of  the  elliptic 
motion.  After  long  and  laborious  efforts,  Nkavton  was 
enabled  to  demonstrate  rigorously  that  this  law  also  re- 
sulted from  the  law  of  the  inverse  square,  and  could  result 
from  no  other.  Thus  all  mystery  disappeared  from  the 
celestial  motions  ;  and  planets  were  shown  to  be  simply 
heavy  bodies  moving  according  to  the  same  laws  tliat  were 
acting  here  around  us,  only  under  very  different  circum- 
stances. All  three  of  Kepler's  laws  were  embraced  in 
the  single  law  of  gravitation  toward  the  sun.  The  sun 
attracts  the  planets  as  the  earth  attracts  bodies  here 
around  us. 

Mutual  Action  of  the  Flanets. — It  remained  to  extend 
and  prove  the  theory  by  considering  the  attractions  of  the 
planets  themselves.  i3y  Newton's  third  law  of  motion, 
each  planet  must  attract  the  sun  with  a  force  equal  to  that 
which  the  sun  exerts  upon  the  planet.  The  moon  also 
must  attract  the  earth  as  much  as  the  earth  attracts  the 
moon.  Such  being  the  case,  it  must  be  highly  probable 
that  the  planets  attract  each  other.  If  so,  Kepler's  laws 
can  only  be  an  approximation  to  the  truth.  The  sun, 
being  immensely  more  massive  than  any  of  the  planets, 
overpowers  their  attraction  upon  each  other,  and  makes 
the  law  of  elliptic  motion  very  nearly  true.  But  still  the 
comparatively  small  attraction  of  the  planets  must  cause 
some  deviations.  Now,  deviations  from  the  pure  elliptic 
motion  were  known  to  exist  in  the  case  of  several  of  the 
planets,  notably  in  that  of  the  moon,  which,  if  gravitation 
were  universal,  must  move  under  the  influence  of  the  com- 
bined atti'action  of  the  earth  and  of  the  sun.  Newton, 
therefore,  attacked  the  complicated  problem  of  the  deter- 
mination of  the  motion  of  the  moon  under  the  combined 
action  of  these  two  forces.  He  showed  in  a  general  way 
that  its  deviations  would  be  of  the  same  nature  as  those 
shown  by  observation.  But  the  complete  solution  of  the 
problem,  which  required  the  answer  to  bo  expressed  iu 
numbers,  was  beyond  his  power. 


othJ 


ticlj 
sul 


"''''^^tiUHBT'" 


ATTRACTION  OF  GRAVITATION. 


139 


sUiptic 
)N  was 
Iso  re- 
l  result 
)m  the 
simply 
at  were 
jircum- 
aced  in 
'he  sun 
iS  here 

extend 
18  of  the 
motion, 
1  to  that 
oon  also 
•acts  the 
probable 
sr's  laws 
Che  sun, 

planets, 
id  makes 

still  the 
tist  cause 
re  elliptic 
•al  of  the 
ravitation 

the  com- 
Newton, 
the  deter- 
combined 
mend  way 
I  as  those 
ion  of  the 
pressed  in 


Gravitation  Besides  in  each  Particle  of  Matter. — Still 
another  question  arose.     Were  these  mutually  attractive 
forces  resident  in  the  centres  of  the  several  bodies  attracted, 
or  in  each  particle  of  the  matter  composing  them  ?    New- 
ton showed  that  the  latter  must  be  the  case,  because  the 
smallest  bodies,    as  well  as  the  largest,  tended   to  fall 
toward  the  earth,  thus  showing  an  equal  gravitation  in 
every  separate  part.      The   question  then   arose  :    what 
would  be  the  action  of  the  earth  upon   a  body  if  the 
body  was  attracted— not  toward  the  centre  of  the  earth 
alone,  but  toward  every  particle  of  matter  in  the  earth  'i 
It  was  shown  by  a  quite  simple  mathematical  demonstra- 
tion that  if  a  planet  were  on  the  surface  of  the  earth  or 
outside  of  it,  it  would  be  attracted  with  the  same  force^as 
if  the  whole  mass  of  the  earth  were  concentrated  in  ite 
centre.     Putting  together  the  various  residts  thus  arrived 
at,  Newton  was  able  to  formulate  his  great  law  of  uni- 
versal gravitation  in  these  comprehensive  words  :  *'  Every 
particle  of  matter  m  the  immeree  at^acta  every  other 
particle  with  a  f&rce  directly  as  the  masses  of  the  two 
particles,  and  vrwersely  as  the  square  of  the  distance 
which  separates  them.^^ 

To  show  the  nature  of  the  attractive  forces  among 
these  various  particles,  let  us  represent  by  m  and  m'  the 
masses  of  two  attracting  bodies.  We  may  conceive  the 
body  w  to  bo  composed  of  m  particles,  and  the  other 
body  to  be  composed  of  m'  particles.  Let  us  conceive  that 
each  particle  of  the  one  body  attracts  eadi  particle  of  the 

other  with  a  force  -, .    Then  every  particle  of  m  will  be 

r 
attracted  by  each  of  the  m'  particles  of  the  other,  and 
therefore  the  total  attractive  force  on  each  of  these  m  par- 
ticles will  be  'i    Each  of  the  m  particles  being  cquaUy 
subject  to  this  attraction,  the  total  attractive  force  between 


the  two  bodies  will  be 


turn 


When   a  given  force  acts 


J 


ASTRONOMY. 


r 


„po„  a  body.  H  will  pK^oce  1-.™>"„K  ^ 

be  ^«  ;  and  couvcrBely  the  accelerating  force  acting  on  the 
body  m  will  be  represented  by  the  fraction  -^. 

§  3.    PBOBLEMB  OP  QBAVITATIOW. 

The  problem  solved  by  I.  K^^^^ 
eBt  genemlity,  was  ^^^^.^^^^^^H^^^^^^  and 

are  given  are  P^J^.^  ^^  "^'^  ^^^  u^  ^  motion  under 
with  certain  velocities.     W  hat  wm  ^  ^ 

the  influence  of  t^-r  mutual  gravi^^aU^j  J^^^^^^ 

tive  motiondcH.  -^-^^J^jf^^^^^^         of  g^avit; 
will  each  revolve  around  tneir  commv/  o 

^l^hpe,  aainthecaseof  planetaiT-^^^^ 

ever,  the  illative  velocity  «^«^^^^*^^S,g  ^„nd  the 
bodies  will  separate  f^-J^^^^j^f^^^^^ 
common  centre  of,g^«;f  f /^"^X^  in  the  case  where 
These  curves  are  found  o  be  ^™^'^  hj^^bolas  when 
the  velocity  is  exac^^  at  *^  ^^tr^urvrmay  be  de- 
the  velocity  exceeds  it.  ^J^LZ^^  the  two  bodies 
scribed,  the  common  centre  of  g^a^  «*  ^^  ^^^^^ 
will  be  in  the  focus  of  the  curve  ^^^^^^^^^^^.^^ 
to  two  bodies,  the  problem  admits  of  a  perfectly  ngo 

mathematical  solution.  rv^Hem  of  planetary 

Having  succeeded  in  solvi^he  p^bl^  of  p^,^  J 

motion  for  the  case  of  *7«  ^^'.HfieTa  rimilar  solu- 
temporaries  very  natumlly  desired  to  effee^a  «nn 

mimber  of  Iwdies  ,  ana  nav  ug  ^^^ 

two  bodies,  it  was  necessary  next  to  try  tnai 


•HI 


larger  the 
lal  to  the 
the  body 
jcts  on  the 
lotion,  will 

iiig  on  the 


in  its  great- 
the  masses 
Bctions,  and 
otion  under 
I  their  rela- 
mount,  they 
B  of  gravity 
3.  If,  how- 
mit,  the  two 
around  the 
ite  branches. 
J  case  where 
erbolas  when 
may  be  de- 
etwo  bodies 
en  restricted 
jctly  rigorous 

of  planetary 
and  his  con- 
i  similar  solu- 
em  of  motion 
;ion  of  a  great 
in  the  case  of 
that  of  three. 


PROBLEMS  OF  GRAVITATION. 


HP 


141 


Thus  arose  the  celebrated  problem  of  three  bodies.     It  is 
fonnd  that  no  rigorous  and  general  solution  of  this  problem 
is  possible.     The  curves  described  by  the  several  bodies 
would,  in  general,  be  so  complex  as  to  defy  mathematical 
definition.     But  in  the  special  case  of  motions  in  the  solar 
system,  the  problem  admits  of  being  solved  by  approxima- 
tion with  any  required  degree  of  accuracy.     The  princi- 
ples involved  in  this  system  of  approximation  may  be  com- 
pared to  those  involved  in  extracting  the  square  root  of 
any  number  which  is  not  an  exact  square  ;  2  for  instance. 
The  square  root  of  2  cannot  be  exactly  expressed  either 
by  a  decimal  or  vulgar  fraction  ;  but  by  incretaing  the 
number  of  figures  it  can  be  expressed  to  any  required  limit 
of  approximation.     Thus,  the  vulgar  fractions  |,  |J,  fH, 
etc.,  are  fractions  which  approach  more  and  more  to  the 
required  quantity  ;  and  by  using  larger  numbers  the  errors 
of  such  fraction  may  be  made  as  small  as  we  please.    So,  in 
using  decimals,  we  diminish  the  error  by  one  tenth  for  eve- 
ry decimal  we  add,  but  never  reduce  it  to  zero.    A  process 
of  the  same  nature,  but  immensely  more  complicated,  has 
to  be  used  in  computing  the  motions  of  the  planets  from 
then-  mutual  gravitation.     The  possibility  of  such  an  ap- 
proximation arises  from  the  fact  that  the  planetary  orbits 
are  nearly  circular,  and  that  their  masses  are  very  small 
compared  with  that  of  the  sun.    The  first  approximation 
is  that  of  motion  in  an  ellipse.     In  this  way  the  motion  of 
a  planet  through  several  revolutions  can  nearly  always  be 
predicted  within  a  small  fraction  of  a  degree,  though  it 
may  wander  widely  in  the  course  of  centuries.    Then  sup- 
pose each  planet  to  move  in  a  known  ellipse  ;  their  mutual 
attraction  at  each  point  of  their  respective  orbits  can  be 
expressed  by  algebraic  f ormulie.    In  constructing  these 
formulsB,  the  orbits  are  first  supposed  to  be  circular  ;  and 
afterward  account  is  taken  by  several  successive  steps  of 
the  eccentricity.    Having  thus  found  approximately  their 
action  on  each  other,  the  deviations  from  the  pure  eUiptic 
motion  produced  by  this  action  may  be  approximately  cal- 


hi 


•  r- 


1 1 


149 


ASTROIfOMT. 


ciliated.  This  being  done,  tlic  motionfl  will  bo  more  exact- 
ly duteriiiinod,  and  the  niutnal  action  can  be  niui'e  exactly 
calcnlated.  Thus,  the  process  can  be  carried  on  step  by 
step  to  any  degree  of  precision  ;  but  an  enormous  amount 
of  calculation  \&  necessary  to  satisfy  the  requirements  of 
modern  times  with  respect  to  precision.*  As  a  general 
rule,  every  successive  step  in  the  approximation  is  much 
more  laborious  than  all  the  preceding  ones. 

To  understand  the  principle  of  astronomical  investiga* 
tion  into  the  motion  of  the  planets,  the  distinction  be- 
tween observed  and  theoretical  motions  must  be  borne  in 
mind.  When  the  astronomer  with  his  meridian  circle  de- 
termines the  position  of  a  planet  on  the  celestial  sphere, 
that  position  is  an  obseiTcd  one.  When  ho  calculates  it,  for 
the  same  instant,  from  theory,  or  from  tables  founded  on 
tlie  theory,  the  result  will  be  a  calculated  or  theoretical 
position.  The  two  are  to  be  regarded  as  separate,  no  mat- 
ter if  they  should  be  exactly  the  same  in  reality,  because 
they  have  an  entii*ely  different  origin.  But  it  must  be  re- 
membered that  no  position  can  be  calculated  from  theory 
alone  independent  of  observation,  because  all  soimd  theory 
requires  some  data  to  start  with,  which  observation  alone 
can  furnish.  In  the  case  of  planetary  motions,  these  data 
are  the  elements  of  the  planetary  orbit  already  described, 
or,  which  amounts  to  the  same  tiling,  the  velocity  and  di- 
rection of  the  motion  of  the  planet  as  well  as  its  mass  at 
some  given  time.  If  these  quantities  were  once  given 
with  mathematical  precision,  it  would  be  possible,  from  the 
theory  of  gravitation  alone,  without  recourse  to  observa- 
tion, to  predict  the  motions  of  the  Janets  day  by  day 
and  generation  after  generation  with  an^  required  degree 
of  precision,  always  supposing  that  they  are  subjected  to  no 
influence  except  their  mutual  gravitation  according  to  the 
law  of  Newton.  But  it  is  impossible  to  determine  the 
elements  or  the  velocities  without  recourse  to  observation  ; 

*  In  the  works  of  the  great  mathematicians  on  this  subject,  algcbruic 
formolee  extending  tlmraj^  many  pages  are  sometimns  given. 


and 
for  1 
then 
mus 
mat] 
obse 
than 
obsei 
80  tr 
their 
W 
mer] 
he  cc 
aseri 
futur 
he  de 
he  mi 
termi 
oretic 
will  « 
the  d 
may  I 
throu 
its  pi 
some 
comn 
omer 
havin 
struci 
toler 
possilj 
latioi 
tirelj 
only 
vices  I 
way 
table 


--"T--t  -'—--■-'•■• 


PROBLEMS  OF  GRAVITATION. 


143 


0  exact- 
exactly 

step  by 
amount 

leuts  of 
general 

is  much 

ivestiga- 
ition  be- 
borne  in 
jirclo  dc- 
,  sphere, 
tes  it,  for 
anded  on 
leoretical 
,  no  mat- 
,  because 
ast  be  re- 
im  theory 
Qd  theory 
ion  alone 
these  data 
iescribed, 
ty  and  di- 
itB  mass  at 
nee  given 
I,  from  the 
)  observa- 
ly  by  day 
■ed  degree 
sctedtono 
ling  to  the 
ermine  the 
^servation  ; 

|ect,  algebraic 
ren. 


and  however  correctly  they  may  seeiiiingly  be  (letcriiiineil 
for  the  time  being,  subHcquent  obscrvatiouH  alwiiyH  bIiow 
them  to  have  been  more  or  less  in  error.  The  reader 
must  understand  that  no  astronomical  observation  can  be 
mathematically  exact.  Both  the  instruments  and  the 
observer  are  subjected  to  influences  which  prevent  more 
than  an  approximation  being  attained  from  any  one 
observation.  The  great  art  of  the  astronomer  consists  in 
80  treating  and  "  bining  his  observations  as  to  eliminate 
their  err.  ,  anu  ».  •  a  result  as  near  the  >  '  at  possible. 
When,  by  thus  bumbining  his  observati.,-*,  the  astrono- 
mer has  obtained  the  elements  of  the  planet's  motion  which 
he  considers  to  be  near  the  truth,  he  calculates  from  them 
a  series  of  positions  of  the  planet  from  day  to  day  in  the 
future,  to  be  compared  with  subsequent  observations.  If 
he  desires  his  work  to  be  more  pennanent  in  its  nature, 
he  may  construct  tables  by  which  the  position  can  be  de- 
termined at  any  future  time.  Having  thus  a  series  of  the- 
oretical or  calculated  places  of  the  planet,  he,  or  others, 
will  compare  his  predictioas  with  observation,  and  from 
the  differences  deduce  corrections  to  his  elements.  We 
may  say  in  a  rough  way  that  if  a  planet  has  been  observed 
through  a  certain  number  of  years,  it  is  possible  to  calculate 
its  place  for  an  equal  number  of  years  in  advance  with 
some  approach  to  precision.  Accurate  observations  are 
commonly  supposed  to  conamence  with  Beadley,  Astron- 
omer Eoyal  of  England  in  1750.  A  century  and  a  quarter 
having  elapsed  since  that  time,  it  is  now  possible  to  con- 
struct tables  of  the  planets,  which  we  may  expect  to  be 
tolerably  accurate,  until  the  year  2000.  But  this  is  a 
possibility  rather  than  a  reality.  The  amount  of  calcu- 
lation required  for  such  work  is  so  immense  as  to  be  en- 
tirely beyond  the  power  of  any  one  person,  and  hence  it  is 
only  when  a  mathematician  is  able  to  command  the  ser- 
vices of  others,  or  when  several  mathematicians  in  some 
way  combine  for  an  object,  that  the  best  astronomical 
tables  can  hereafter  be  constructed. 


AaTRONOMT. 


%  4.    RESULTS  OP  GRAVITATION. 

From  what  we  have  said,  it  wiU  Ihj  Been  that  the  problem 
of  the  motions  of  the  planets  under  the  influence  of  grav- 
itation has  caUed  forth  all  the  skill  of  the  mathematicians 
who  have  attacked  it.    They  actually  find  themselves  able 
to  reach  a  solution,  which,  so  far  as  the  mathematics  of  the 
subject  are  concerned,  may  be  true  for  many  centuries,  but 
not  a  solution  which  shall  be  true  for  all  time      Among 
those  who  have  brought  the  solution  so  near  to  perfec- 
tion, La  Place  is  entitled  to  the  firstrank,  although  there 
are  others,  especiaUy  La  Gbangk,  who  are  fully  worthy  o 
L  named  aloVg  with  him.     It  will  be  of  interest  to  state 
the  general  results  reached  by  these  and  other  mathema- 

^'''mcall  to  mind  that  but  for  the  attraction  of  the 
planets  upon  each  other,  every  planet  would  move  around 
the  sun  hi  an  invariable  ellipse,  according  to  Kbplebs 
laws  The  deviations  from  this  elliptic  motion  proved 
bv  their  mutual  attraction  are  called  perturhaiiom.  When 
they  were  investigated,  it  was  found  that  they  were  of  two 
claies,  wliich  were  denominated  respectively  perwdtc 
perturbatiom  mi  seGular  variations. 

The  periodic  pert^bations  consist  of  oscillations  depend- 
ent  upon  the  mutual  positions  of  the  ^ets,  and  there- 
fore of  comparatively  short  period.    Whenever  after  a 
number  of  revolutions,  two  planets  return  to  the  same 
nosition  in  their  orbits,  the  periodic  perturbations  are  of 
^e  same  amount  so  far  as  these  two  planets  are  concerned. 
They  may  therefore  be  algebraically  expressed  ««.  depend- 
ent upon  the  longitude  of  the  two  planets,  the  d«t™;^>ng 
one  and  the  disturbed  one.    For  instance,  the  jwrturba- 
tions  of  the  earth  produced  by  the  action  of  M^cury 
depend  on  the  longitude  of  the  earth  and  on  that  of Jfjr- 
eZ.    Those  produced  by  the  attraction  of   ^^^ /e- 
pS  upon  the  longitude  of  the  earth  and   on  that  of 
Vervus,  and  so  on. 


seni 


the 
Let 
ano 
the 
one 
lim 
mo 
son 


RESULTS  OF  OBAVITATIOir. 


145 


problem 
of  grav- 
naticians 
Ives  able 
cs  of  the 
iries,  but 
Among 
)  perfec- 
igh  there 
<rorthy  to 
it  to  state 
uathema- 

•n  of  the 
ire  around 
Kbplbb's 
produced 
18.  When 
ere  of  two 
•  periodic 

18  depend- 
md  there- 
er,  after  a 

the  same 
)n8  are  of 
concerned, 
as  depend- 
disturbing 
»  perturba- 
l  Mercury 
lat  of  Mer- 

Vemu  de- 
ou  that  of 


The  sefitil^r perturbations,  or  secular  variations  as  they 
are  commonly  called,  consist  of  slow  changes  in  the  forms 
and  positions  of  the  several  orbits.  It  is  found  that  the 
perihelia  of  all  the  orbits  are  slowly  changing  their  ap- 
parent directions  from  the  sun  ;  that  the  eccentricities  of 
some  are  increasing  and  of  others  diminishing  ;  and  that 
the  positions  of  the  orbits  are  also  changing. 

One  of  the  first  questions  which  arose  in  reference  to 
these  secular  variations  was,  will  they  go  on  indefinitely  ? 
If  they  should,  they  would  evidently  end  in  the  subversion 
of  the  solar  system  and  the  destruction  of  all  life  upon  the 
earth.  The  orbits  of  the  earth  and  planets  would,  in  the 
course  of  ages,  become  so  eccentric,  that,  approaching 
near  the  sun  at  one  time  and  receding  far  away  from  it  at 
another,  the  variations  of  temperature  would  be  destruc- 
tive to  life.  This  problem  was  first  solved  by  La  Gbanob. 
He  showed  that  the  changes  could  not  go  on  forever,  but 
that  each  eccentricity  would  always  be  confined  between 
two  quite  narrow  limits.  His  results  may  be  expressed 
by  a  very  simple  geometrical  construction.  Let  8  repre- 
sent the  sun  situated  iu  the  focus  of  the  ellipse  in  which 


the  planet  moves,  and  let  C  be  the  centre  of  the  ellipse. 
Let  a  straight  line  SB  emanate  from  the  sun  to  B, 
another  line  pass  from  BtoD,  and  so  on  ;  the  number  of 
these  lines  being  equal  to  that  of  the  planets,  and  the  last 
one  terminating  in  C,  the  centre  of  the  ellipse.  Then  the 
line  S  B  will  be  moving  around  the  sun  with  a  very  slow 
motion ;  B  D  will  move  around  B  with  a  slow  motion 
somewhat  different,  and  so  each  one  will  revolve  in  the 


146 


AHTRONOMY. 


same  manner  until  wo  micl.  the  lino  which  carncs  on  its 
end  the  centre  oi  the  ellipne.     The«o  m..tH.n«  are  «<>  «low 
that  Bi.me  of  them  rciuire  tenn  of  thonsaiu  h,  and  otherH 
hundreds  of  thoiiBands  of  years  to  perform  the  revolution. 
By  the  combined  motion  of  them  all,  the  centre  of  the 
ellipse  deBcribcH  a  somewhat  irregular  curve.     It  i8  ov» 
dent,  however,  that  the  distance  of  the  centre  froin  the 
sun  ian  never  be  greater  than  the  mm  of  these  revolving 
lines      Now  this  distance  shown  the  eccentricity  of  the 
ellipse,  which  is  equal  to  half  the  difference  between  the 
greatest  and  least  distances  of  the  planet  from  the  sun. 
The  perihelion  being  in  the  direction  6'.^,  on  the  opposite 
Bide  of  the  sun  from  C,  it  is  evident  that  the  motion  of 
(7  will  carry  the  perihelion  with  it.     It  is  found  m  this 
way  that  the  eccentricity  of  the  earth's  orbit  has  been 
diminishing  for  about  eighteen  thousand  years,  and  will 
continue  to  diminish  for  twenty-five  thousand  years  to 
come,  when  it  will  be  more  neariy  circular  than  any  orbit 
of  our  system  now  is.     But  before  becoming  quite  circu- 
lar,  the  eccentricity  will  begin  te  increase  again,  and  so  go 
on  oscillating  indefinitely. 

Seoular  Aooeleration  of  the  Moon.—  Another  remark- 
able  result  reached  by  mathematical  research  is  that  of  the 
acceleration  of  the  moon's  motion.    More  than  a  century 
ago  it  was  found,  by  comparing  the  ancient  and  modern 
Nervations  of  the  moon,  that  the  ktter  moved  around  the 
earth  at  a  slightly  greater  rate  than  she  did  m  ancient 
times.     The  existence  of  this  acceleration  was  a  source  of 
groat  perplexity  to  La  Geanob  and  La  Place,  because 
Lv  thought  that  they  had  demonstrated  mathematically 
that  the  attraction  could  not  have  accelerated  or  retarded 
the  mean  motion  of  the  moon.    But  on  continuing  his  m- 
vestigation,  La  Place  found  that  there  was  one  cause 
which  he  omitted  to  take  account  of-namely,  the  secular 
diminution  in  the  eccentricity  of  the  earth  «   orbit    ^^ 
which  we  have  just  spoken.     He  found  that  this  change 
in  the  eccentricity  would  slightly  alter  the  action  of  the 


ACt'KI.KHATlON  Ot    TUB  MOON. 


U1 


arrics  on  itB 
are  «<>  slow 
and  other» 
revolution, 
mtro  of  the 
It  18  ovi 
re  from  the 
BO  revolving 
icity  of  the 
between  the 
oni  the  sun. 
the  opposite 
le  motion  of 
)und  in  this 
tit  has  been 
ars,  and  will 
ind  years  to 
tan  any  orbit 
5  quite  circu- 
in,  and  so  go 

;her  remark- 
is  that  of  the 
an  a  century 
and  modem 
;d  around  the 
id  in  ancient 
as  a  source  of 
.ACE,  because 
lathematically 
d  or  retarded 
inning  his  in- 
ras  one  cause 
[y,  the  secular 
;h'B   orbit,  of 
it  this  change 
action  of  the 


Bun  upon  the  moon,  and  that  this  alteration  of  action 
would  l>e   such   that  so   long  as   the  eccentricity  grew 
smaller,  the  motion  of  the  moon  would  continue  to  be  ac- 
celerated.   Computing  the  moon's  acceleration,  he  found  it 
to  be  e(iual  to  ten  seconds  into  the  square  of  the  numlxsr 
of  centuries,  the  law  being  the  same  m  tliat  for  the  motion 
of  a  falling  body.    That  is,  while  in  one  century  she  would 
1)6  ten  seconds  ahead  of  the  place  she  would  have  occupied 
had  her  mean  motion  l)een  uniform,  she  would,  in  two 
centuries,  be  forty  seconds  ahead,  in  three  centuries  ninety 
seconds,  and  so  on  ;  and  during  the  two  thousand  years 
which  have  elapsed  since  the  observations  of  Hipi'archus, 
the  acceleration  would  be  mote  than  a  degree.     It  has  re- 
cently been  found  that  La  Place's  calculation  was  not  com- 
plete, and  that  with  the  more  exact  motliods  of  recent  times 
the  real  acceleration  computed  from  the  theory  of  gravita- 
tion is  only  about  six  seconds.  The  observations  of  ancient 
eclipses,  however,  compared  with  our  modem  tables,  show 
an  acceleration  greater  than  this  ;  but  owing  to  the  rade 
and  doubtful  character  of  nearly  all  the  ancient  data,  there 
is  some  doubt  about  the  exact  amount.     From  the  most 
celebrated  total  eclipses  of  the  sun,  an  acceleration  of  about 
twelve  seconds  is  deduced,  while  the  observations  of 
Ptolemy  and  the  Arabian  astronomers  indicate  only  eight 
or  nine  seconds.     Tliere  is  thus  an  apparent  discrepancy 
between  theory  and  observation,  the  latter  giving  a  larger 
value  to  the  acceleration.    This  diflEerence  is  now  accounted 
for  by  supposing  that  the  motion  of  the  earth  on  its  axis 
is  retarded— that  is,  that  the  day  is  gradually  growing 
longer.     From  the  modem  theory  of  friction,  it  is  found 
that  the  motion  of  the  ocean  under  the  influence  of  the 
moon's  attraction  which  causes  the  tides,  must  be  accom- 
panied with  some  friction,  and  that  this  friction  must  re- 
tard the  earth's  rotation.     There  is,  however,  no  way  of 
determining  the    amount  of   this  retardation  unless  we 
assume  that  it  causes  the  observed  discrepancy  between 
the  theoretical  and  observed  accelerations  of  the  moon. 


■r-" 


! 


148 


AHTUoNoMir. 


Tlow  tliis  uffwt  in  imnhKHMl  will  ho  won  hy  ruflvcting  that 
if  thu  (liiy  iHrontinuully  growing  longiti'  without  our  know- 
ing it,  uiir  obflorvutions  of  tlic  nuMin,  whicli  wu  niuy  H(ip|M)M! 
to  bo  madu  at  noon,  for  oxanijtlo,  will  l)c  couHtantly  niado  a 
little  later,  becauHO  the  interval  from  one  noon  to  another 
will  be  continually  growing  a  little  longer.  The  moon  con- 
tinually moving  forward,  the  ol)6orvation  will  place  her  fur- 
ther and  further  ahead  than  she  would  have  been  observed 
had  there  l)een  no  retardation  of  the  time  of  noon.  If  in 
the  course  of  ages  our  noon-dials  get  to  l)e  an  hour  too 
late,  wr  nliould  find  the  moon  ahead  of  her  calculated  place 
by  one  hour's  motion,  or  about  a  degree.  The  present 
theory  of  acceleration  is,  therefore,  that  the  moon  is  really 
accelerated  al)out  six  seconds  in  a  century,  and  that  the 
motion  of  the  earth  on  its  axis  is  gradually  diminishing 
at  such  a  rate  as  to  produce  an  apparent  additional  ac- 
celeration which  may  range  from  two  to  six  seconds. 


§  5.    REKABKS   ON  THE  THEORY  OF   OBAVITA- 

TIOK. 

The  real  nature  of  the  great  discovery  of  Newton  is  so 
frequently  misunderstood  that  a  little  attention  may  be 
given  to  its  elucidation.  Gravitation  is  frequently  spoken 
of  as  if  it  were  a  theory  of  Newton's,  and  very  generally 
received  by  astronomers,  but  still  linble  to  be  idtimately 
rejected  as  a  great  many  other  theories  have  beeu.  Not 
infrequently  people  of  greater  or  less  intelligence  are 
found  making  great  efforts  to  prove  it  erroneous.  Every 
prominent  scientific  institution  in  the  world  frequently 
receives  essays  having  this  object  in  view.  Now,  the  fact 
is  that  Newton  did  not  discover  any  new  force,  but  only 
showed  that  the  motions  of  the  heavens  could  be  accounted 
for  by  a  force  which  we  all  know  to  exist.  Gravitation 
(Latin  graviteu — weight,  heaviness)  is,  properly  speaking, 
tlio  force  which  makes  all  bodies  here  at  the  surface  of  the 
earth  tend  to  fall  downward  ;  and  if  any  one  wishes  to 


HU 

in, 

th 

th 

on 

to 

itta 

of 

foi 

tht 

J 

gra 

doi 

is. 

exp 

as  I 

thai 

line 

dev 

tioE 

on(! 

it  is 

con| 

for 

no 

unil 

witi 


oui 


HKALITY  OF  OllAVITATIoy. 


14i) 


cting  tliat 
nir  know- 

tly  made  a 
to  another 
moon  con- 
co  her  f  ur- 
m  observed 
)on.    Hin 
in  hour  too 
dated  place 
'he  present 
on  is  really 
id  that  the 
dhninishing 
ditional  ac- 
icouds. 


OBAVTPA- 

Jewton  is  BO 
tion  may  be 
lently  spoken 
ery  generally 
)e  ^dtimately 
B  beeu.    Not 
elligence  are 
eouB.    Every 
Id  frequently 
Kow,  the  fact 
orce,  but  only 
dbe  accounted 
Gravitation 
)erly  speaking, 
5  surface  of  the 
one  wishes  to 


Htibvort  the  theory  of  gravitation,  he  uiust  l)Ogin  by  prov- 
ing tliftt  this  force  does  not  exist.  This  no  one  would 
think  of  doing.  What  Nkwton  did  was  to  show  that 
this  force,  which,  before  his  time,  had  been  recognized 
only  as  acting  on  the  surface  of  the  earth,  really  extended 
to  the  heavens,  and  that  it  resided  not  only  in  the  earth 
itself,  but  in  the  heavenly  bodies  also,  and  in  each  particle 
of  matter,  however  situated.  To  put  the  matter  in  a  terse 
form,  what  Nkwton  discovered  was  not  (/ra/oitatian,  but 
the  nniversality  of  gravitation. 

It  may  bo  inquired,  is  the  induction  which  supposes 
gravitation  universal  so  complete  iis  to  be  entirely  beyond 
doubt  ?    We  reply  that  within  the  solar   /stem  it  certainly 
is.     The  laws  of  motion  as  established  by  observation  and 
experiment  at  the  surface  of  the  earth  nmst  be  considered 
as  mathematically  certain.      Now,  it  is  an  ooserved  fact 
that  tha  planets  in  their  motions  deviate  from  ^a-aight 
lines  in  a  certain  way.    By  the  first  law  of  motion,  such 
deviation  can  be  protluced  caly  by  a  force  ;  and  the  dire, 
tion  and  intensity  of  this  force  admit  of  being     ilcnlated 
once  that  the  motion  is  determined.    When  thus  <  siho  lated, 
it  is  found  to  be  exactly  represented  by  one  great  force 
constantly  directed  toward  the  sun,  and  smaller  subsidiary 
forces  directed  toward  the  several  planets.      Therefore, 
no  fact  in  nature  is  more  firmly  estabhshed  than  is  that  of 
universal  gravitation,  as  laid  down  by  Newton,  at  least 
within  the  solar  system. 

We  shall  find,  in  describing  double  stars,  that  gravita- 
tion is  also  found  to  act  between  the  components  of  a  great 
number  of  such  stars.  It  is  certain,  therefore,  that  at 
least  some  stars  gravitate  toward  each  other,  as  the  bodies 
of  the  solar  system  do  ;  but  the  distance  which  separates 
most  of  the  stars  from  each  othe"  rani  from  our  sun  is  so 
immense  that  no  evidence  of  gravitation  between  them 
has  yet  been  given  by  observation.  Still,  that  they  do 
gravitate  according  to  New  ■Jj's  law  can  hardly  be  seri- 
ously doubted  by  any  one  v  ho  understands  the  subject. 


160 


ASTBONOMT. 


The  reader  may  now  be  supposed  to  see  the  absurdity  of 
supposing  that  the  theory  of  gravitation  can  ever  be  sub- 
verted. It  is  not,  however,  absurd  to  suppose  that  it  may 
yet  be  shown  to  be  tlie  result  of  some  more  general  law. 
Attempts  to  do  this  are  made  from  time  to  time  by  iiM:n 
of  a  philosophic  spirit ;  but  thus  far  no  theory  of  the  sub- 
ject having  the  sUghtest  probability  in  its  favor  lias  been 

propounded.  i       •     • 

Perhaps  one  of  the  most  celebrated  of  these  theories  is 
that  of  George  Lewis  Le  Sage,  a  Swiss  physicist  of  the 
last  century.  He  supposed  an  infinite  number  of  ultra- 
mundane corpuscles,  of  transcendent  minuteness  and  veloc- 
ity, traversing  space  in  straight  lines  in  all  tUrections.  A 
smgle  body  placed  in  the  midst  of  such  an  ocean  of  mov- 
ing corpuscles  would  remain  at  rest,  sino«  it  would  be  equal- 
ly impelled  in  overy  direction.  But  two  bodies  would  ad- 
vance toward  each  other,  because  each  of  them  would 
screen  the  other  from  these  corpuscles  moving  in  the 
straight  line  joining  their  centres,  and  there  would  be  a 
slight  excess  of  corpuscles  acting  on  that  side  of  each 
body  which  was  turned  away  from  the  other.* 

One  of  the  commonest  conceptions  to  account  for  grav- 
itation is  that  of  a  fluid,  or  ether,  extending  through  all 
space,  which  is  supposed  to  be  animated  by  certain  vibra- 
tions, and  forms  a  vehicle,  as  it  were,  for  the  transmission 
of  gravitation.     This  and  all  other  theories  of  the  kind 
are  subject  to  the  fatal  objection  of  proposing  complicated 
systems  to  account  for  the  most  simple  and  elementary 
facts.     If,  indeed,  such  systems  were  otherwise  known  to 
exist,  and  if  it  could  be  shown  that  they  really  would 
produce  the  effect  of  gravitation,  they  would  be  entitled 
to  recei»tion.     But  since  they  have  been  imagined  only  to 
account  for  gravitation  iteolf,  and  since  there  is  no  proof 
of  their  existence  except  that  of  accounting  for  it,  they 

*  Reference  may  be  made  to  nn  article  on  the  kinetic  theories  of 
gravitation  by  William  B.  Taylor,  in  the  Smithsonian  Report  for 
1876. 


i 


p  I  fi 


CAU8B  OP  GRAVITATION. 


VSi 


dity  of 
be  sub- 
it  may 
•al  law. 

I)y  \VA:Xi 

ho  sitb- 
asbeen 

iories  is 
;  of  the 
f  ultra- 
d  veloc- 
m&.  A 
of  mov- 
e  equal - 
[)uld  ad- 
i  would 
in  the 
aid  be  a 
of  each 

'or  grav- 
ough  all 
in  vibra- 
ismission 
;he  kind 
iplicated 
smentary 
mown  to 
ly  would 
entitled 
d  only  to 
no  proof 
•  it,  they 

theories  of 
Report  for 


are  not  entitled  to  any  weight  whatever.  In  the  present 
state  of  science,  we  are  justified  in  regarding  gravitation  as 
an  ultimate  principle  of  mattfcv,  incapable  of  alteration  by 
any  transformation  to  which  matter  can  be  subjected. 
The  most  careful  experiments  show  that  no  chemical  pro- 
cess to  which  matter  can  be  subjected  either  increases  or 
diminishes  its  gravitating  principles  in  the  slightest  degree. 
We  cannot  therefore  see  how  this  principle  can  ever  be 
referred  to  any  more  general  cause. 


CHAPTER  VI. 

THE  MOTIONS  AND  ATTRACTION  OF  THE  MOON. 

Each  of  the  planets,  except  Mercury  and  Vmua,  is  at- 
tended  by  one  or  more  satellites,  or  moms  as  they  are  some- 
times familiarly  called.   These  objects  revolve  around  their 
several  planets  in  nearly  circular  orbits,  accompanying  them 
in  their  revolutions  around  the  sun.     Their  distances  from 
their  planets  are  very  small  compared  with  the  distances 
of  the  latter  from  each  other  and  from  the  sun.     Iheir 
magnitudes  also  are  very  small  compared  with  those  of  the 
planets  around  which   they  revolve.     Where  there  are 
several  satellites  revolving  around  a  planet,  the  whole  of 
thflse  bodies  forms  a  small  system  similar  to  the  solar  sys- 
'^  in  arrangement.     Considering  each  system  by  itself, 
the  satellites  revolve  around    their  central    planets  or 
"  primaries,"  in  nearly  circular  orbits,  much  as  the  planete 
revolve  around  the  sun.     But  each  system  is  carried  around 
the  sun  without  any  serious  derangement  of  the  motion 
of  its  several  bodies  among  themselves. 

Our  earth  has  a  single  satellite  accompanjang  it  in  this 
way,  the  familiar  moon.  It  revolves  around  the  earth  m 
a  little  less  than  a  month.  The  nature,  causes  and  con- 
sequences of  this  motion  form  the  subject  of  the  present 
chapter. 


§  1. 


THE  MOOW'B   MOTIONS   AHD   PHASES. 


That  the  moon  performs  a  monthly  circuit  in  the  heav- 
ens is  a  fact  with  which  we  are  all  familiar  from  child- 
hood.    At  certain  times  we  see  her  newly  emerged  from 


MOTION  OF  THE  MOON. 


168 


OON. 

is  at- 
8ome- 
1  their 
r  them 
B  from 
stances 
Their 
of  the 
jre  are 
lole  of 
lar  sys- 
r  itself, 
lets  <»• 
planets 
around 
motion 

in  this 
earth  in 
nd  con- 
present 


lie  heav- 
n  child- 
ed  from 


the  snn's  rays  in  the  western  twilight,  and  then  we  call 
her  the  new  moon.  On  each  succeeding  evening,  we  see 
her  further  to  the  east,  so  that  in  two  weeks  she  is  oppo- 
site the  sun,  rising  in  the  east  as  he  sets  in  the  west. 
Continuing  her  course  two  weeks  more,  she  has  approached 
the  sun  on  the  other  side,  or  from  the  west,  and  is  once 
more  lost  in  his  rays.  At  the  end  of  twenty-nine  or  thirty 
days,  we  see  her  again  emerging  as  new  moon,  and  her  cir- 
cuit is  complete.  It  is,  however,  to  be  remembered 
that  the  sun  hsis  been  apparently  moving  toward  the  east 
among  the  stars  during  the  whole  month,  so  that  during 
the  interval  from  one  new  moon  to  the  next  the  moon  has 
to  make  a  complete  circuit  relatively  to  the  stars,  and 
move  forward  some  30°  further  to  overtake  the  sun.  The 
revolution  of  the  moon  among  the  stars  is  perfonned  in 
about  27i  days,*  so  that  if  we  observe  when  the  moon  is 
very  near  some  star,  we  shall  find  her  in  the  same  position 
relative  to  the  star  at  the  end  of  this  interval. 

The  motion  of  the  moon  in  this  circuit  differs  from  the 
appareni  motions  of  the  planets  in  being  always  forward. 
We  have  seen  that  the  planets,  though,  on  the  whole,  mov- 
ing directly,  or  toward  the  east,  are  affected  with  an  ap- 
parent retrograde  motion  at  certain  intervals,  owing  to  the 
motion  of  the  earth  around  the  sun.  But  the  earth  is  the 
real  centre  of  the  moon's  motion,  and  carries  the  moon 
along  with  it  in  its  annual  revolution  around  the  styi.  To 
fonn  a  correct  idea  of  the  real  motion  of  these  three 
bodies,  we  must  imagine  the  earth  performing  its  circuit 
around  the  sun  in  one  year,  and  carrying  with  it  the  moon, 
which  makes  a  revolution  around  it  in  27  days,  at  a  distance 
only  about  ^^  that  of  the  sun. 

In  Fig.  55  suppose  S  to  represent  the  sun,  the  large 
circle  to  represent  the  orbit  of  the  earth  around  it,  E  to 
bie  some  position  of  the  earth,  and  the  dotted  circle  to  rep- 
resent the  orbit  of  the  moon  around  the  earth.     We  must 

*  More  exactly.  27*  82166. 


154 


A8TR0N0MT. 


imagine  the  latter  to  carry  this  circle  with  it  in  its  an- 
nual course  around  the  sun.  Suppose  that  when  the  earth 
is  at  ^  the  moon  is  at  M.     Then  if  the  earth  move  to 

El  in  27^  (lays,  the  moon 
will  have  made  a  complete 
revolution  relative  to  the 
stars — that  is,  it  will  be  at 
M„  the  line  E^  J/,  being  par- 
allel to  EM.  But  new 
moon  will  not  have  arrived 
again  because  the  sun  is  not 
in  the  same  direction  as  lie- 
fore.  The  moon  must  move 
through  the  additional  arc 
Jf,  EM^,  and  a  little  more, 
owing  to  the  continual  ad- 
vance of  the  earth,  before  it 
will  again  1)6  new  moon. 
Phasea  of  the  Moon. — The  moon  being  a  non-luminous 
body  shines  only  by  reflecting  the  light  falling  on  her 
from  some  other  body.  The  principal  source  of  light  is 
the  sun.  Since  the  moon  is  spherical  in  shape,  the  sun 
can  illuminate  one  half  her  surface.  The  appearance  of 
the  moon  varies  according  to  the  amount  of  her  illumi- 
nated hemisphere  which  is  turned  toward  the  earth,  as 
can  bf  seen  by  studying  Fig.  56.  Here  the  central 
globe  is  the  earth ;  the  circle  around  it  represents  the  orbit 
of  the  moon.  TLo  rays  of  the  sun  fall  on  both  earth  and 
moon  from  the  right,  the  distance  of  the  sun  being,  on  the 
scale  of  the  flgure,  some  30  feet.  Eight  positions  of  the 
moon  are  shown  around  the  orbit  at  A,  E,  C,  etc.,  and 
the  right-hand  hemisphere  of  the  moon  is  illuminated  in 
each  position.  Outside  these  eight  positions  are  eight 
others  showing  how  the  moon  looks  as  seen  from  the  earth 
in  each  position. 

At  .4   it  is  "  new  moon,"   the  moon  being  nearly 
between  the  earth  and  the  sun.     Its  dark  hemisphere 


PHASES  OF  THE  MOON. 


155 


its  an- 
B  earth 
lOve  to 

moon 
iinplete 
to    the 

be  at 
ng  par- 
it    new 
arrived 
n  is  not 
n  as  be- 
st move 
inal  arc 
B  more, 
raal  ad- 
jefore  it 
oon. 
iiminous 

on  her 
:  light  is 

the  sun 
trance  of 
r  illumi- 
earth,  as 
!  central 
the  orbit 
iarth  and 
g,  on  the 
ns  of  the 
etc.,  and 
inated  in 
are  eight 
the  earth 

ig  nearly 
emisphore 


is  then  turned  toward  the  earth,  so  that  it  is  entirely 
invisible. 

At  ^'the  observer  on  the  earth  sees  about  a  fourth  of 
the  illuminated  hemisphere,  which  looks  like  a  crescent, 
as  shown  in  the  outside  figure.  In  this  position  a  great 
deal  of  light  is  reflected  from  the  earth  to  the  moon,  ren- 
dering the  dark  part  of  the  latter  visible  b}  a  gray  light. 


Vis.  cm. 


"old  moon  in 


This  appearance  is  sometimes  called  the 
the  new  moon's  arms.'' 

At  C  the  moon  is  said  to  be  in  hrr  '*  first  quarter,"  and 
one  half  l»er  illmninated  hemisphere  is  visible. 

At  O  three  fourths  of  the  illuminated  hemisphere  is 
visible,  and  at  B  the  whole  of  it.  The  latter  position,  when 
the  moon  is  opposite  the  sun,  is  called  '*  full  moon." 

After  this,  at  H,  2>,  F^  the  same  appearances  are  re- 
peated in  the  reversed  order,  the  position  D  being  called 
the  "last  quarter." 


156 


ASTRONOMY. 


The  four  principal  phases  of  the  moon  are,      New 
mo^!"  "  Fi4  quarter,"  "  Full  moon,"  "  Last  quarter, 
which  occur  in  regt.lar  and  unending  succession,  at  mter- 
vals  of  between  7  and  8  days. 

§2.    THE   SUN'S   DISTURBmO  FOBOB. 

The  distances  of  the  sun  and  planets  being  so  immensely 
great  compared  with  that  of  the  moon,  their  attraction 
STn  the  JLrth  and  the  moon  is  at  all  times  very  neariy 
Zal.     Now  it  is  an  elementary  principle  of  mechan  cs 
th^if  two  bodies  are  acted  upon  by  equal  and  paraM 
forces    no  matter  how  great  these  forces  may  be,  the 
bo2  will  move  relatively  to  each  other  as  if  those  orces 
did  not  act  at  all,  though  of  course  the  absolute  moUon  of 
each  will  be  different  from  what  it  otherwise  would  be. 
If  we  calculate  the  absolute  attraction  of  the  sun  «pon  the 
moon  we  shall  find  it  to  be  about  twice  as  great  as  that  of 
r^rtZ  tea-,  although  it  is  situated  at  400  tim^  the 
distance,  its  mass  is  al^out  330,000  times  as  great  as  that  of 
the  earth,  and  if  we  divide  this  mass  by  the  square  of  the 
distance  400  we  have  2  as  the  quotient.  ,.n,„.,^ 

To  those  unacquainted  with  mechanics,  the  difficulty 
often  suggests  itself  that  the  sun  ought  to  draw  the  moon 
away  f i^m  the  earth  entirely.  But  we  are  to  remember 
that  thesun  attracts  the  earth  in  the  same  way  that  it  at- 
tracts  tSe  moon,  so  that  the  difference  between  the  sun  s 
attraction  on  the  moon  and  on  the  earth  is  only  a  smaU 
fraction  of  the  attraction  between  the  earth  and  the  moon 

As  a  consequence  of  these  forces,  the  moon  moves  around 
the  earth  nearly  as  if  neither  of  them  were  attracted  by 

•In  this  comparison  of  the  attractive  forces  of  the  sun  "poiLthe 
moon  and  upon  the  earth,  the  reader  will  remember  that  we  are  8p«.k- 
Sr^JSf  the  a6«««te  force,  but  of  what  is  called  the  '^'^'^l^"'^' 
which  is  properly  the  ratio  of  the  absolute  force  to  the  mass  of  he 
SatrST  The  earth  haying  80  times  the  mass  of  the  moon  the 
s^sltf  course  attract  it  with  80  Umes  tlfe  ateolute  force  in  order 
to  produce  the  same  motion,  or  the  same  accelerating  force. 


SUN'H  ATTRACTION  ON  MOON. 


1B7 


the  sun — that  is,  nearly  in  an  ellipse,  having  the  earth  in 
its  focus.  But  there  is  always  a  small  difference  between 
the  attractive  forces  of  the  sun  upon  the  moon  and  upon  the 
earth,  and  this  difference  constitutes  a  disturbing  force 
which  makes  the  moon  deviate  from  the  elliptic  orbit 
which  it  would  otherwise  describe,  and,  in  fact,  keeps  the 
ellipse  which  it  approxhnately  describes  in  a  state  of  con- 
stant change. 

A  more  precise  idea  of  the  manner  in  which  the  sun  disturbs  the 
motion  of  the  moon  around  the  earth  majr  be  gathered  from 
Fig.  57.  Here  8  represents  the  sun,  and  the  circle  F  Q  ^  JV  repre- 
sents the  orbit  of  the  moon.  First  suppose  the  moon  at  N,  the  posi- 
tion corresponding  to  new  moon.  Then  the  moon,  being  nearer  to 
the  sun  than  the  earth  is,  will  be  attracted  more  powerfully  by  it 
than  the  earth  is.  It  will  therefore  be  drawn  away  from  the  earth, 
or  the  action  of  the  sup  will  tend  to  separate  the  two  bodies. 


Pig.  67. 

Next  suppobo  the  anon  at  ^the  position  corresponding  to  full 
moon.    Here  the  action  of  the  sun  upon  the  earth  will  bo  more 

Sowerful  than  upon  the  moon,  and  the  earth  will  in  consecjOence  be 
rawn  away  from  the  moon.  In  this  position  also  the  effect  of  the 
disturbing  force  is  to  separate  the  two  bodies.  If,  on  the  other 
hand,  the  moon  is  near  the  first  quarter  or  near  Q,  the  sun  will  exert 
a  nearly  equal  attraction  on  both  bodies ;  and  ince  the  lines  of  at- 
traction E  S  and  Q  8  then  convergt'  toward  8,  it  follows  that  there 
will  be  a  tendency  to  bring  the  two  bodies  together.  The  same 
will  evidently  be  true  at  the  third  quarter.  Hence  the  influence  of 
the  disturbing  force  changes  back  and  forth  twice  in  the  course  of 
each  lunar  month. 

The  disturbing  force  in  question  may  be  constructed  for  any  po- 
sition of  the  moon  in  iia  orbit  in  the  following  way,  which  is  be- 
lieved to  be  due  to  Mr.  R.  A.  Pkoctok  :  Let  3f  be  the  position  of 
the  moon  ;  let  us  represent  the  sun's  attraction  upon  it  by  the  line 
M  8,  and  let  us  investigate  what  line  will  represent  the  sun's  attrac- 
tion upon  the  earth  on  the  same  scale.    From  Jf  drop  the  perpen- 


Ui  )1 


15g  A8TR0N0M7. 

have, 

Attrmctionon  tmrth  _  SM 

Attraction  on  moon      S  E ' 
We  have  taken  the  line  8  M  it-elf  to  represent  the  attraction  on 
the  moon,  so  that  we  have 

Attraction  on  moon  =  8M. 
Multiplying  the  two  equations  member  by  member,  we  And, 

Attraction  on  earth  =  S  Ji  x  ^-gi- 

The  line  S  Af  is  nearly  equal  to  8  P,  so  that  we  may  take  for  an 
approximation  to  the  required  line. 


sr 


8F 
'8'E 


=  8P^ 


SP* 


{SP+PEf 


_    =zSP 


1 


(}^8P) 


PE 


the  last  equation  being  obtained  by  the  binomial  theorm.  But 
the  fraction  ^  is  so  small,  being  less  than  ^,  that  lU  p«we« 
above  the  first  will  be  small  enough  to  be  neglected.  8o  we  shall 
have  for  the  required  hne, 

ap—^EP. 


MOON'S  N0DK8. 


160 


,     This 
re  shall 


the  bodies  together  at  the  quarten.  Conaeauentlv,  upon  the  whole, 
the  tendency  of  the  sun's  attraction  is  to  diminish  the  attraction  of 
the  earth  upon  the  moon. 


ction  on 


«1, 


le  for  an 


D' 


rm. 


But 


bs  powers 
}  we  shall 


equal  to  2 
ae  scale  be 
;h  we  seek 
»f  the  sun 
I.  If  then 
le  opporite 
will  repre- 
omposition 

mple  nuin- 
lie  moon  is 
■bing  force 
the  moon. 

KAnUiBIf 
ich  tends 
}ay  the  line 
ly  from  the 
hich  draws 


g  8.    MOnOCT  OF  THS  MOOirS  NODSI. 

Among  tho  changt«  which  the  snn's  attraction  produces 
in  the  moon's  orbit,  Oiat  which  interests  ns  most  is  the 
constant  variation  in  the  pUne  of  the  orbit.  This  plane 
is  indicated  by  tho  path  which  Xu'^  moon  seems  to  describe 
in  its  circuit  around  the  celestial  sphere.  Simple  naked 
eye  estimates  of  the  moon's  position,  continued  during  a 
month,  would  show  that  her  path  was  always  quite  near 
the  ecliptic,  l)ecause  it  would  be  evident  to  the  eye  that, 
like  the  sun,  she  was  much  farther  north  while  passing 
from  the  vernal  to  the  autumnal  equinox  than  while  de- 
scribing the  other  half  of  her  circuit  from  the  autumnal 
to  the  vernal  equinox.  It  would  be  seen  that,  like  the 
sun,  she  was  farthest  north  in  about  six  hours  of  right  as- 
cension, and  farthest  south  when  in  about  eighteen  hours 
of  right  ascension. 

To  map  out  the  path  with  greater  precision,  we  have  to 
observe  the  position  of  the  moon  from  night  to  night  with 
a  meridian  circle.  We  thus  lay  down  her  course  among 
the  stars  in  the  same  manner  that  we  have  formerly  shown 
it  possible  to  lay  down  the  sun's  path,  or  the  ecliptic.  It 
is  thus  found  that  the  path  of  the  moon  may  be  considered 
as  a  great  circle,  making  an  angle  of  5°  with  the  ecliptic, 
and  crossing  the  ecliptic  at  this  small  angle  at  two  oppo- 
site points  of  the  heavens.  These  points  are  called  the 
moon's  nodea.  The  point  at  which  she  passes  from  the 
south  to  the  north  of  the  ecliptic  is  called  the  ascending 
node;  that  in  which  she  passes  from  the  north  to  the 
south  is  the  descending  node.  To  illustrate  the  motion  of 
the  moon  near  the  node,  the  dotted  line  a  a  may  be  taken 
as  showing  the  path  of  the  moon,  while  the  circles  show 
her  position  at  successive  intervals  of  one  hour  as  she  is  ap- 
proaching her  ascending  node.  Position  number  9  is  exactly 


IfiO 


ABTnOirOMT. 


end 
wo 
bIio 
the 


at  the  node.     H   we 
continue  following  her 
course  in  this  way  for 
a  week,  wo  should  find 
that    she   had   moved 
about  90°,  and  attained 
her  greatest  north  lati- 
tude at  5°   from  the 
ecliptic.     At  the 
of  another  week, 
should    find    that 
had  returned     to 
ecliptic  and  crossed  it 
at  her  descending  node. 
At  the  end  of  the  third 
week  very  nearly,  we 
should  find  that  she  had 
made  three  fourths  the 
circuit  of  the  heavens, 
and  was  now  in   her 
greatest  south  latitude, 
being  5°  south  of  the 
ecliptic.     At  the  end 
of  six  or  seven  days 
more,  we  should  again 
find  her   crossing  the 
ecliptic  at  her  ascend- 
ing node  as  before.  We 
may  thus  conceive  of 
four  cardinal  points  of 
the  moon's  orbit,  90° 
apart,  marked  by  the 
two  nodes  and  the  two 
points  of  greatest  north 
and  south  latitude. 

Motion  of  the  Nodes. 
—A  remarkable  prop- 


r 


f    we 
g  licr 
ly  for 
dliml 
iioved 
tallied 
h  lati- 
n  the 
0  end 
k,   wo 
dX  she 
0     the 
SBcd  it 
r  node, 
e  third 
ly,  wo 
iho  had 
ths  tho 
Qavons, 
in   hor 
ititudo, 

of  the 
he  end 
m  days 
Id  again 
ing  the 
ascond- 
)re.  We 
seive  of 
oints  of 
bit,  90° 

by  the 
the  two 
est  north 
nde. 

lo  Nodes. 
>le  prop- 


MOONS  NO  DBS. 


161 


orty  of  these  points  is  tliat  they  are  not  Hxed,  btit  are  uoiu 
Btantly  moving.  The  general  motion  ia  a  little  irregnlar, 
but,  leaving  out  small  irregularities,  it  is  constantly  toward 
the  west.  Thus  returning  to  our  watch  of  the  course  of 
the  moon,  we  should  find  that,  at  her  next  return  to  the 
ascending  node,  she  would  not  describe  the  lino  a  a  as 
before,  but  the  line  hh  nbuut  one  fourth  of  a  diameter 
north  of  it.  She  would  therefore  reach  the  ecliptic  more 
than  1^°  west  of  the  preceding  point  of  crossing,  and  her 
(tther  cardinal  points  would  be  found  1^°  farther  west  as 
she  went  around.  On  her  noxt  return  she  would  dcscribo 
the  lino  CO,  then  tho  line  dd,  etc.,  indefinitely,  each  line 
l)eing  farther  toward  the  west.  The  figure  shows  the 
paths  in  five  consecutive  returns  to  tho  node. 

A  lapse  of  nine  years  will  bring  the  descending  node 
around  to  the  place  which  was  before  occupied  by  the 
ascending  node,  and  thus  wo  shall  have  the  moon  crossing 
at  a  small  inclination  toward  the  south,  as  shown  in  the 
figure. 

A  complete  revolution  of  the  nodes  takes  place  in  18.6 
years.  After  the  lapse  of  this  period,  the  motion  is  re- 
peated in  tlie  same  manner. 

One  consequence  of  this  motion  is  that  the  moon,  after 
leaving  a  node,  reaches  the  saTue  node  again  sooner  than 
she  completes  her  true  circuit  in  the  heavens.  How  much 
sooner  is  readily  computed  from  the  fact  that  tho  retro- 
grade motion  of  the  node  amounts  to  1°  26'  31'  daring 
the  period  that  tho  moon  is  returning  to  it.  It  takes  the 
moon  about  two  hours  and  a  half  (more  exactly  O**.  10944) 
to  move  through  this  distance  ;  consequently,  comparing 
with  the  sidereal  period  already  given,  we  find  that  the 
return  of  the  moon  to  her  node  takes  place  in  27''.  82166 
—  O"*.  10944  =  27*.  21222.  This  time  will  be  important  to 
us  in  considering  the  recurrence  of  eclipses. 

In  Fig.  59  is  illustrated  the  effeot  of  these  changes  in 
the  jwBition  of  the  moon's  orbit  upon  lior  motion  rela- 


t 


leu 


ASTRONOMY. 


tivo  to  the  equator.   E  hero   ropre«enU  the  vernal  and 
uve  lo  mn  «H  ^  ^j^^  autunnml  eqninox,  situated 

180°    apart.     In    March,    1876, 
the  moon's  aucending  node  cor- 
responded with  the  vernal  equi- 
nox,  and  her  descending   node 
with  the  autumnal  one.     Conse- 
quently she  was  6°  north  of  the 
ecliptic  when    in    six  hours  of 
right  ascension  or  near  the  mid- 
dle   of    the    figure.     Since  the 
ecliptic    is    23r  north    of    the 
equator  at  this  point,  the  moon  at- 
tained a  maximum  declination  of 
284°;  she  therefore  passed  nearer 
the   zenith   when  in   six  hours 
of  right  ascension  than  at  any 
other  time  during  the  eighteen 
years'  period.     In  the  language 
of  the  almanac,  "  the  moon  ran 
high."     Of  course  when  at  her 
greatest  distance   south  of   the 
equator,  in  the  other  half  of  her 
orbit,  she  attained  a  correspond- 
ing  south  declination,  and  cul- 
minated at  a  lower  altitude  than 
she  had  for  eighteen  years.    In 
1886  the  nodes  will  change  places, 
and  the  orbit  will  deviate  from 
the  equator  less  than  at  any  other 
time  during  the  eighteen  years. 
In  1880  the  descending  node  will 
be  in  six  hours  of  right  ascension, 
and  the  greatest  angular  distance 

of  the  moon  from  the  equator 

will  be  nearly  equal  to  that  of  the  sun. 


*a(K7i=-iw^ 


PKHiailK  OF  TIIK  MOON. 


183 


ftl  and 
it  dated 

1876, 
lo  cor- 
I  eqni- 
;  node 
Conso- 
of  the 
mre  of 
le  inid- 
ice  the 
of    the 
toon  at- 
ition  of 
i  nearer 
t  hours 

at  any 
)ighteen 
angaage 
oon  ran 
I  at  her 

of   the 
If  of  her 
respond- 
and  cul- 
ude  than 
ears.     In 
^  places, 
ate  from 
any  other 
en  years, 
node  will 
ascension, 
\r  distance 
e  equator 


^  4.    MOTION  OF  THB  FIBIOBB. 

If  the  sun  uxurtod  no  disturbing  force  on  the  moon,  the 
latter  would  move  round  the  earth  in  an  oUipse  according 
to  Kki'lek's  laws.  But  the  difference  of  the  sun's  attrac- 
tion on  the  earth  and  on  the  moon,  though  only  a  small 
fraction  uf  the  earth's  attractive  force  on  the  moon,  is  yet 
so  great  as  to  produce  deviations  from  the  elliptic  motion 
very  much  greater  than  occur  in  the  motions  of  the  planets. 
It  also  produces  rapid  changes  in  the  elliptic  orbit.  The 
most  remarkable  of  these  changes  are  the  progressive 
motion  of  the  nodus  just  described  and  a  corresponding 
motion  of  the  pcrigoo.  Referring  to  Fig.  62,  which  illus- 
trated the  elliptic  orbit  of  a  planet,  let  us  suppose  it  to 
represent  the  orbit  of  the  moon.  8  will  then  represent 
the  earth  instead  of  the  sun,  and  n  will  be  the  Xxmax per- 
igee, or  the  point  of  the  orbit  nearest  the  earth.  But, 
instead  of  remaining  nearly  fixed,  as  do  the  orbits  of  the 
planets,  the  lunar  orbit  itself  may  be  considered  as  making 
a  revolution  round  the  earth  in  about  nine  years,  in  the 
same  direction  as  the  moon  itself.  Hence  if  we  note  the 
longitude  of  the  moon's  perigee  at  any  time,  and  again 
two  or  three  years  later,  wo  shall  find  the  two  positions 
quite  different.  If  we  wait  four  years  and  a  half,  we  shall 
find  the  perigee  in  directly  the  opposite  point  of  the 
heavens. 

The  eccentricity  of  the  moon's  orbit  is  about  0.056,  and 
in  consequence  the  moon  is  about  6°  ahead  of  its  mean 
place  when  90°  past  the  perigee,  and  about  the  same  dis- 
tance behind  when  half  way  from  apogee  to  perigee. 

The  disturbing  action  of  the  sun  produces  a  great  num- 
ber of  other  inequalities,  of  which  the  largest  are  the 
eoectian  and  the  variation.  Tlie  former  is  more  than  a 
degree,  and  the  latter  not  much  lees.  The  formulee  by 
which  they  are  expressed  belong  to  Celestial  Mechanics, 
and  the  reader  who  desires  to  study  them  is  referred  to 
works  on  that  subject. 


1U4 


ASTRONOMY. 


§  5.    EOTATION  OP  THE  MOON. 

The  moon  rotates  on  her  axis  in  the  same  time  and  in 
the  same  direction  in  which  she  revolves  around  tlie  earth. 
In  consequence  she  always  presents  very  nearly  the  same 
face  to  the  earth.*  There  is  indeed  a  small  oscillation 
called  the  libt-ation  of  the  moon,  arising  from  the  fact  that 
her  rotation  on  her  axis  is  uniform,  while  her  revolution 
around  the  earth  is  not  uniform.  In  consequence  of 
this  we  sometimes  see  a  little  of  her  farther  hemisphere 
first  on  one  side  and  then  on  the  other,  but  the  greater 
part  of  this  hemisphere  is  forever  hidden  from  human 

The  axis  of  rotation  of  the  moon  is  inclmed  to  the 
ecliptic  about  1°  29'.  It  is  remarkable  that  this  axis 
changes  its  direction  in  a  way  corresponding  exactly  to 
the  motion  of  the  nodes  of  the  moon's  orbit.  Let  us  sup- 
pose a  line  passing  through  the  centre  of  the  earth  per- 
pendicular to  the  plane  of  the  moon's  orbit.  In  conse- 
quence of  the  inclination  of  the  orbit  to  the  ecUptic,  this 
line  will  point  5°  from  the  pole  of  the  ecliptic.  Then, 
suppose  another  line  parallel  to  the  moon's  axis  of  rota- 
tion. This  line  will  intersect  the  celestial  sphere  1°  29' 
from  the  pole  of  the  ecliptic,  and  on  the  opposite  side 
from  the  pole  of  the  moon's  orbit,  so  that  it  will  bo  6i° 
from  the  latter.  As  one  pole  revolves  around  the 
pole  of  the  ecliptic  in  18.6  years,  the  other  wiU  do  the 
same,  always  keeping  the  same  position  relative  to  the 
first. 


•  This  conclusion  is  often  a  pons  aaiwrum,  to  some  who  conceive 
that,  if  the  swne  face  of  the  moon  ia  always  presented  to  the  earth,  she 
cannot  rotate  at  all.  The  difficulty  arises  from  a  misunderstaudmg  of 
the  difference  between  a  relative  and  an  absolute  rotation.  It  is  true 
that  she  does  not  rotate  relatively  to  the  line  drawn  from  the  earth  to 
hef  centre,  but  she  must  rotate  relative  to  a  fixed  line,  or  a  line  drawn 
to  a  fixed  star. 


line  and  in 
i  the  earth, 
y  the  same 
oscillation 
le  fact  that 
•  revolution 
equence  of 
hemisphere 
the  greater 
■om  human 

ned  to  the 
it  this  axis 
5  exactly  to 
Let  us  sup- 
)  earth  per- 
In  conse- 
jcliptic,  this 
itic.  Then, 
xie  of  rota- 
Aero  1°  29' 
pposite  side 
;  will  bo  6i° 
around  the 
will  do  the 
ative  to  the 


who  conceive 
a  the  earth,  she 
iderstauding  of 
tion.  It  is  true 
}m  the  earth  to 
w  a  line  drawn 


THE  TIDES. 


105 


§  6.    THE  TIDES. 

The  ebb  and  flow  of  the  tides  are  produced  by  the  un- 
equal attraction  of  the  sun  and  moon  on  different  parts  of 
the  earth,  arising  from  the  fact  that,  owing  to  the  magni- 
tude of  the  earth,  some  parts  of  it  are  nearer  these  attracting 
bodies  than  others,  and  are  therefore  more  strongly  at- 
tracted.    To  understand  the  nature  of  the  tide-producing 
force,  we  must  recall  the  principle  of  mechanics  already 
cited,  that  if  two  neighboring  bodies   are  acted  on  by 
equal  and-  parallel  accelerating  forces,  their  motion  rel- 
ative to  each  other  wiil  not  be  altered,  because  both  will 
move  equally  under  the  influence  of  the  forces.     When 
the  forces  are  slightly  different,  either  in  magnitude  or 
direction  or  both,  the  relative  motion  of  the  two  bodies 
will  depend  on  this  difference  alone.     Since  the  stin  and 
moon  attract  those  parts  of  the  earth  which  are  nearest 
them  more  powerfully  than  those  which  are  remote,  there 
arises  an  inequality   which  produces   a    motion  in   the 
waters  of  the  ocean.     As  the  earth  revolves  on  its  axis, 
different  parts  of  it  are  brought  in  in  succession  under  the 
moon.     Thus  a  motion  is  produced  in  the  ocean  which 
goes  through  its  rise  and  fall  according  to  the  apparent 
position  of  the  moon.     This  is  called  the  tidal  wme. 

The  tide-producing  force  of  the  sun  and  moon  is  so  nearly  like 
the  disturbing  force  of  the  sun  upon  the  motion  of  the  moon  around 
the  earth  that  nearly  the  same  explanation  will  apply  to  both.  iiCt 
us  then  refer  again  to  Pig.  57.  and  suppose  i  to  represent  the 
centre  of  the  earth,  the  circle  FQNxU  circumference,  M  a  par- 
tide  of  waver  on  the  earth's  surface,  and  8  either  the  sun  or  the 

"^The  entire  earth  being  rigid,  each  part  of  it  will  move  under  the 
influence  of  the  moon's  attraction  as  if  the  whole  were  concen- 
trated  at  its  centre.  But  the  attraction  of  the  moon  «pon  the 
Darticle  M,  being  different  from  its  mean  attraction  on  the  earth,  will 
ffi  to  m^ke  it  move  differently  from  the  earth. ,  The  *o«e  wtadi 
causes  this  difference  of  motion,  as  already  explained,  ^llJe'«P«- 
sented  by  the  line  MA.  It  is  true  that  this  same  distuibing  force  is 
Tcting  ujon  that  portion  of  the  solid  earth  at  if  as  well,  as  upon  t  e 
water    But  the  elwth  cannot  yield  on  account  of  its  ngidity  ;  the 


, 


166 


ASTnONOMT. 


water  therefore  tends  to  flow  along  the  earth's  surface  from  M 
toward  N.  There  is  therefore  a  residual  force  tending  to  make  the 
water  higher  at  N  than  at  M. 

If  we  suppose  the  particle  M  to  be  near  F,  then  the  point  A  will 
be  to  the  left  of  F.  The  water  will  therefore  be  drawn  in  an  oppo- 
site direction  or  toward  F.  There  will  therefore  also  be  a  force 
tending  to  make  the  water  accumulate  around  F.  As  the  disturb- 
ing force  of  the  sun  tends  to  cause  the  earth  and  moon  to  separate 
both  at  new  and  full  moon,  so  the  tidal  force  of  the  sun  and 
moon  upon  the  earth  tends  to  make  the  waters  accumulate  both  at 
M  and  F.  More  exactly,  the  force  in  question  tends  to  draw  the 
earth  out  into  the  form  of  a  prolate  ellipsoid,  having  its  longest 
axis  in  the  direction  of  the  attracting  boay.  As  the  earth  rotates 
on  its  axis,  each  particle  of  the  ocean  is,  in  the  course  of  a  day, 
brought  in  to  the  four  positions  N  Q  F  R,  or  into  some  positions 
corresponding  to  these.  Thus,  the  tide-producing  force  changes 
back  and  forth  twice  in  the  course  of  a  lunar  day.  (By  a  lunar  day 
we  mean  the  interval  between  two  successive  passages  of  the  moon 
acrosdthe  meridian,  which  is,  on  the  average,  about  24**  48".)  If  the 
waters  could  yield  immediately  to  this  force,  we  should  always  have 
high  tide  at  ^and  JVand  low  tides  at  Q  and  R.  But  there  are  two 
causes  which  prevent  tliis. 

1.  Owing  to  the  inertia  of  the  water,  the  force  must  act  some 
time  before  the  full  amount  of  motion  is  produced,  and  this  motion, 
once  attained,  will  continue  after  the  force  has  ceased  to  act. 
Again,  the  waters  will  continue  to  accumulate  as  Icng  as  th^re  is 
any  motion  in  the  required  direction.  The  result  of  this  would  be 
high  tides  at  Q  and  R  and  low  tides  at  F  and  N,  if  the  ocean 
covered  the  earih  and  were  perfectly  free  to  move.  That  is,  high 
tides  would  then  be  six  hours  after  the  moon  crossed  the  meridian. 

2.  The  principal  cause,  however,  which  interferes  with  the 
regularity  of  the  motion  is  the  obstruction  of  islands  and  continents 
to  the  free  motion  of  the  water.  These  deflect  the  tidal  wave  from 
its  course  in  so  many  different  ways,  that  it  is  hardly  possible  to 
trace  the  relation  between  the  attraction  of  the  moon  and  the  mo- 
tion of  the  tide ;  the  time  of  high  and  low  tide  must  therefore  be 
found  by  observing  at  each  point  along  the  coast.  By  comparing 
these  times  through  a  series  of  years,  a  very  accurate  idea  of  the 
motion  of  the  tidal  wave  can  bo  obtained. 

Such  observations  have  been  made  over  our  Atlantic  and  Pacific 
coasts  by  the  Coast  Survey  and  over  most  of  the  coasts  of  Europe, 
by  the  countries  occupying  them.  Unfortunately  the  tides  cannot 
be  observed  away  from  the  land,  and  heace  little  is  known  of  the 
coarse  of  the  tidal  wave  over  the  ocean. 

We  have  remarked  that  both  the  sun  and  moon  exert  a 
tide-producing  force. ^^That  of  the  sun  is  aI>out  ^  of  that 
of  the  moon,  ^^tloew  and  full  moon  the  two  forces  are 
united,  and  4;he  actual  force  is  equal  to  their  sum 


first 
thej 
a  hi 
and 
new 
tide 
the 
duct 
moo 
aftei 
est  8 
new 
tion, 
threi 
uallj 
T] 
lems 
seve: 
less  I 
plan! 
wlii( 
at  d 
tum 
havt 
sofi 
tidei 
whi( 
give 
cons 
give 
obse 
are 
the 
cffe< 


At 


THK  TIDEa. 


167 


ace  from  M 
to  make  tlie 

point  A  will 
.  in  an  oppo- 

0  be  a  force 
the  disturb- 
n  to  separate 
;he  sun  and 
ilate  both  at 
to  draw  the 
;  its  longest 
earth  rotates 
rse  of  a  day, 
ime  positions 
)rce  changes 
Y  a  lunar  day 

of  the  moon 
48-".)  If  the 
.  always  have 
there  are  two 

ust  act  some 

1  this  motion, 
lased  to  act. 
(ig  as  there  is 
his  would  be 
if  the  ocean 
That  is,  high 
le  meridian, 
res  with  the 
ad  continents 
al  wave  from 
ly  possible  to 

and  the  mo- 
t  therefore  be 
3y  comparing 
te  idea  of  the 

ic  and  Pacific 
its  of  Europe, 
I  tides  cannot 
kaown  of  the 


iQon  exert  a 
it  ^  of  that 
0  forces  are 
ir  sum.     At 


first  and  last  quarter,  when  the  two  bodies  arc  90°  apart, 
tliey  act  in  opposite  directions,  tlie  sun  tending  to  produce 
a  high  tide  where  the  moon  tends  to  produce  a  low  one, 
and  vice  versa'.  The  result  of  this  is  that  near  the  time  of 
new  and  full  moon  we  have  what  are  known  as  the  spring 
tides,  and  near  the  quarters  what  are  called  neap  tides.  If 
the  tides  were  always  proportional  to  the  force  which  pro- 
duces them,  the  spring  tides  would  be  highest  at  full 
moon,  but  the  tidal  wave  tends  to  go  on  for  some  time 
after  the  force  which  produces  it  ceases.  Hence  the  high- 
est spring  tides  are  not  reached  until  two  or  three  days  after 
new  and  full  moon.  Again,  owing  to  the  effect  of  fric- 
tion, the  neap  tides  continue  to  be  less  and  less  for  two  or 
three  days  after  the  first  and  last  quarters,  when  the  grad- 
ually increasing  force  again  has  time  to  make  itself  felt. 

The  theory  of  the  tides  offers  very  complicated  prob- 
lems, which  have  taxed  the  powers  of  mathematicians  for 
several  generations.  These  problems  are  in  their  elements 
less  simple  than  those  presented  by  the  motion?  of  the 
planets,  owinj*  to  the  number  of  disturbing  circumstances 
which  enter  into  them.  The  various  depths  of  the  ocean 
at  different  points,  the  friction  of  the  water,  its  momen- 
tum when  it  is  once  in  motion,  the  effect  of  the  eoast-lines, 
have  all  to  be  taken  into  account.  These  quantities  are 
so  far  from  being  exactly  known  that  the  theory  of  the 
tides  can  be  expressed  onl^  by  some  general  principles 
which  do  not  suffice  to  enable  u^  *o  prfK?;''t  them  for  any 
given  place.  From  observation,  howevor,  it  is  easy  to 
construct  tables  showing  exactly  what  tid*  c  corrsspond  1,o 
given  positions  of  the  sun  and  moor,  at  any  norl  where  tlie 
observations  are  made.  With  such  tables  th  j  ebb  and  flew 
are  predicted  for  the  benefit  of  all  who  *re  interested,  but 
the  results  may  be  a  little  uneert  r'n  on  acccuui  <  f  the 
effect  of  the  winds  upon  the  motion  ov  the  wat'^r. 


CHAPTER  VII. 

ECLIPSES  OF  THE  SUN  AND  MOON 

Eclipses  are  a  class  of  phenomena  arising  from  the 
shadow  of  one  body  being  cast  upon  another,  and  tlius 
wholly  or  partially  obscuring  it.  In  an  eclipse  of  the  sun, 
the  shadow  of  the  moon  sweeps  over  the  earth,  and  the 
sun  is  wholly  or  partially  obscured  to  observers  on  that 
part  of  the  earth  where  the  shadow  falls.  In  an  eclipse  of 
the  moon,  the  latter  enters  the  shadow  of  the  earth,  and  is 
wholly  or  partially  obscured  in  consequence  of  being  de- 
prived of  some  or  all  its  borrowed  light.  The  satellites 
of  other  planets  are  from  time  to  time  eclipsed  in  the 
same  way  by  entering  the  shadows  of  their  primaries  ; 
among  these  the  satellites  of  Jupiter  are  objects  whose 
eclipses  may  be  observed  with  great  regularity. 


g  1.  THE  EABTH'S  SHADOW  AND  PENUHBBA. 

In  Fig.  60  let  8  represent  the  sun  and  E  the  earth. 
Draw  straight  lines,  DB  Fand  D'  W,  each  tivngent 
to  the  sun  and  the  earth.  The  two  bodies  being  supposed 
spherical,  these  lines  will  be  the  intersections  of  a  cone 
with  the  plane  of  the  paper,  and  may  be  taken  to  repre- 
sent that  cone.  It  is  evident  that  the  cone  B  VB'  will 
be  the  outline  of  the  shadow  of  the  earth,  and  that  within 
this  cone  no  direct  sunlight  can  penetrate.  It  is  therefore 
called  the  earth's  shadow  cone. 

Let  us  also  draw  the  lines  D'  B  P  and  D  B'  P'  to  rep- 
resent the  other  cone  tangent  tc  '^e  sun  and  earth.     It  is 


thei 
the 


So  if 

1  = 

the  ci 

r  = 

R  = 

P  = 
8,t 

we  ha 


But  h 


Hence 


The 
tlic  rei 
byobsi 


THE  EARTH'S  SHADOW. 


169 


)0N 

I  from  the 
r,  and  tlius 
of  the  sun, 
th,  and  the 
ere  on  that 
in  eclipse  of 
larth,  and  is 
•f  being  de- 
he  satellites 
psed  in  the 
primaries  ; 
jects  whose 


BnTHBBA. 

i*  the  earth. 
!ach  timgent 
ng  supposed 
IS  of  a  cone 
on  to  repre- 
B  VB'  will 
1  that  within 
;  ia  therefore 

3'  P'  to  rep- 
earth.     It  is 


then  evident  that  within  the  region  V  B  P  and  V B'  P' 
the  light  of  the  sun  will  be  piirtially  but  not  entirely  cut 
off. 


Pig.  60.— form  op  sitadow. 

DimmmoM  of  Shadow.  —Let  us  investigate  the  distance  E  Ffrom 
the  centre  of  tlie  earth  to  the  vertex  of  the  shadow.  Tlie  triangles 
V  E  B  and  V  8  D  axe  similar,  having  a  right  angle  at  B  and  at  D. 
Hence, 

VE:  En  =  VS:SD=  ES:(81}-EBy. 

So  if  we  put 

l—VE,  the  length  of  the  shadow  measured  from  the  centre  of 
the  earth. 
r  =  ES,  the  radius  vector  of  the  earth, 
R=8 D,  the  radius  of  the  sun. 
p  =  EB,  the  radius  of  the  earth, 

8,  the  angular  semi-diameter  of  the  sun  as  seen  front  the  earth, 
ir,  the  horizontal  parallax  of  the  sun, 

we  have 


l=z  VE=z 


ES  X  EB 


rp 
8D  -  EB~  R^-P 

But  hy  the  theory  of  parallaxes  (Chapter  I.,  §  7), 

p  =  r  sin  TT 

£  =  r  sin  8 
Henco, 

1  = 


sin  ^'  —  sm  rr 


The  mean  value  of  the  sun's  angular  semi-diameter,  from  which 
the  real  value  never  differs  by  more  than  the  sixtieth  part,  is  found 
by  observations  to  be  altout  16'  0'  =  960",  while  the  mean  value  of  ir 


1 


iro 


ASTRONOMY. 


is  about  8"  ■  8.    We  find  sin  8-An  rr  =  0 •  00461,  and  -^^^--^j^- 
I       -  217      Wc  tliercforo  conclude  that  tiic  mean  lengtli  of 

'"•  S h™ "(Srfflt  on.  BXtieth  l™  .tan  the  .new  in  D».m- 

earth's  centre  it  ^ill  be  equal  to  (l  -  ?,)p.  for  this  formula  gives 
the  radius  p  when  z  =  0,  and  the  dian.eter  /*ro  when  ^  =  /  as  it 
should.* 

§  2.    ECLIPSES  OP  THE  MOOW. 

The  mean  distance  of  the  moon  from  the  eavtli  is  about 
60  radii  of  the  latter,  while,  as  we  have  jnst  Been,  the 
length  EVoi  the  earth's  ahadow  is  217  radu  ot  the  earth. 
Hete  when  the  moon  passes  through  the  shadow  she  does 
BO  at  a  point  Iobs  than  three  tenths  of  tl»e  way  froin 
E  to  F.    The  radius  of  the  shadow  here  will  be  HVT 
of  the  radius  E  B  oi  the  earth,  a  q.antity  which  we  read- 
ily find  to  be  about  4600  kilometres.     The  radius  of  the 
moon  being  1736  kilometres,  it  will  be  f  tl'^ly.f^.^^'Xi 
by  the  shadow  when  it  passes  through  it  withni  28b4 
kilometres  of  the  axis  i?  Fof  the  shadow.    If  its  least  dis- 
tance from  the  axis  exceed  this  amount,  a  portion  ot  the 
lunar  globe  will  be  outside  the  limits  B  F  of  the  shadow 
cone,  and  will  thoiofonj  receive  a  portion  of  the  direct 
light  of  the  sun.     If  ♦ae  least  distance  of  the  centre  of  the 
nfoon  .^rom  the  uxis  of  the  shadow  is  greater  than  the 
sum  of  the  radii  of  the  moon  and  the  shadow-that  is, 
greater  than  6336  kilomf.t  ea-tho  mooa  will  not  enter  tlic 
*  It  will  bo  noted  that  this  expression  is  not.  rigorouslv  spf^klnp,  the 

greater  than  K  B. 


"  — ~...  rtjUMl 


^1  ::iM4j:-^?-'^-.-..'^ 


T 


ECLTPsm  or  rnK  moon. 


tri 


*(  —  sin  fl- 
n  Icngtii  of 
;  ill  roiiiul 
nean  radius 
n  the  figure 
li  from  the 
,n  in  Decem- 

the  distance 
e  from  the 

rmula  gives 

1  2  =  /  as  it 


•til  is  about 
b  seen,  the 
[  the  eartli. 
)W  she  does 
way  from 

ch  we  read- 
idius  of  the 
^  enveloped 
vithin  2864 
its  least  dis- 
rtion  of  the 
the  shadow 
t  the  direct 
jcntro  of  the 
er  than  the 
ow— that  is, 
lot  enter  the 

y  spottklng,  the 
from  a  point  on 
measured  in  a 
iieter  woiiltl  be 
Duld  be  a  little 


shadow  at  all,  and  there  will  be  no  ellipse  proper,  thongh 
the  brilliancy  of  the  moon  must  be  diminished  wherever 
sho  is  within  the  pennmbral  region. 

When  an  eclipse  of  the  moon  occnrs,  the  phases  are  laid 
down  in  the  almanac  in  the  following  manner  :  Supposing 
the  moon  to  be  moving  aronnd  the  earth  from  below  np- 
ward,  its  advancing  edge  first  meets  the  boundary  B'  P' 
of  the  penumbra.  The  time  of  this  occurrence  is  given  in 
the  almanac  as  that  of  "  moon  entering  penumbra."  A 
small  portion  of  the  sunlight  is  then  cut  off  from  the  ad- 
vancing edge  of  the  moon,  and  this  amount  constantly  in- 
creases until  the  edge  reaches  the  boundary  B'  V  of  the 
shadow.  It  is  curious,  however,  that  the  eye  can  scarcely 
detect  any  diminution  in  the  brilliancy  of  the  moon  ifntil 
she  lias  almost  touched  the  boundary  of  the  shadow.  The 
observer  must  not  therefore  expect  to  detect  the  coming 
eclipse  until  very  nearly  the  time  given  in  the  almanac  as 
that  of  "  moon  entering  shadow."  As  this  happens,  the 
advancing  portion  of  the  lunar  disk  will  be  entirely  lost  to 
view,  as  if  it  were  cut  off  by  a  rather  ill-defined  line.  It 
takes  the  moon  about  an  hour  to  move  over  a  distance 
equal  to  her  own  diameter,  so  that  if  the  eclipse  is  nearly 
central  the  whole  moon  will  be  immersed  in  the  shadow 
about  an  hour  after  she  firt  strikes  it.  This  is  the  time  of 
beginning  of  total  eclipse.  So  long  as  only  a  moderate 
portion  of  the  moon's  disk  is  in  the  shadow,  that  portion 
will  be  entirely  invisible,  but  if  the  eclipse  becomes  total 
the  whole  disk  of  the  moon  will  nearly  always  bo  plainly 
visible,  shining  with  a  red  coppery  light.  This  is  owing  to 
the  refraction  of  the  sun's  rays  by  the  lower  strata  of  the 
earth's  atmosphere.  Wo  shall  see  hereafter  that  if  a  ray  of 
light  D  B  passes  from  tlie  sun  to  the  earth,  so  as  just  to 
graze  the  latter,  it  is  bent  by  refraction  more  than  a  de- 
gree out  of  its  course,  so  that  at  the  distance  of  the  moon 
the  whole  shattow  is  filled  with  this  refracted  liglit.  An 
observer  on  the  mo<m  would,  during  a  total  edijisc  of  tW 
later,  see  the  earth  surrounded  by  a  ring  of  light,  and  riiis 


172 


AsrnoNOMr. 


ring  would  appear  red,  oving  to  the  absorption  of  the  blue 
and  green  rays  by  the  earth's  atmosphere,  just  as  the  sun 
seeins  red  when  setting. 

The  moon  nuiy  remain  enveloped  in  the  shadow  of  the 
earth  during  a  period  ranging  from  a  few  minutes  to  nearly 
two  hours,  according  to  the  distance  at  which  she  passes 
from  the  axis  of  the  shadow  and  the  velocity  of  her  angu- 
lar motion.  When  she  leaves  the  shadow,  the  phases 
which  wo  have  described  occur  in  reverse  order. 

It  very  often  happens  that  the  moon  passes  through  the 
penumbra  of  the  earth  without  touching  the  shadow  at  all. 
No  notice  is  taken  of  these  passages  in  our  almanacs,  be- 
cause, as  akeady  stated,  the  diminution  of  light  is  scarcely 
perceptible  unless  the  moon  at  least  grazes  the  edge  of  the 
shadow. 

§  8.    EC5LIPSBS  OP  THE  SUN. 

In  Fig.  57  we  may  suppose  B I^  B'  to  represent  the 
moon  as  well  as  the  earth.     The  geometrical  theory  of  the 
shadow  will  remain  the  same,  though  the  length  of  the 
shadow  will  be  much  less.     We  may  regard  the  mean 
semi-diameter  of  the  sun  as  seen  from  the  moon,  and  its 
mean  parallax,  as  being  the  same  for  the  mOon  as  for  the 
earth.     Therefore  in  the  formula  which  gives  the  length 
of  the  moon's  shadow  the  denominator  will  retain  the 
same  value,  while  in  the  numerator  we  must  substitute  the 
radius  of  the  moon  for  that  of  the  earth.     The  radius  ot 
the  moon  is  about  1736  kilometres,  or  1080  miles.    Multi- 
plving  this  by  217,  as  before,  we  find  the  mean  length  ot 
[he  moon's  shadow  to  be  377,000  kilometres,  or  235,000 
miles.     This  is  very  nearly  the  same  with  the  distance  ot 
the  moon  from  the  earth  when  she  is  in  conjunction  with 
the  sun.     We  therefore  conclude  that  when  the  moon 
passes  between  the  earth  and  the  sun,  the  former  will  be 
very  near  the  vertex  V  of  the  shadow.     As  a  matter  of 
fact  an  observer  on  the  earth's  surf  ace  will  sometimes  pass 


THE  MOON'S  SItAlJOW. 


178 


the  blue 
the  8un 

V  of  tho 
:o  nearly 
lie  paABCB 
er  aiigu- 
3   phases 

ongh  the 
>w  at  all. 
nacs,  be- 
}  scarcely 
gc  of  the 


csent  the 
>ry  of  the 
;th  of  the 
the  mean 
tn,  and  its 
as  for  the 
bhe  length 
retain  the 
stitute  the 
3  radius  of 
8.    Multi- 
length  of 
,r  235,00() 
distance  of 
iction  with 
the  moon 
ner  will  be 
.  matter  of 
Btimes  pass 


through  the  region  O  VC\  and  sometimes  on  the  other 
side  of  F. 

Now,  in  Fig.  ♦•0,  still  supposing  7?  E  Ji'  to  he  the 
moon,  let  us  draw  the  lines  />  />"  /"  and  JJ'  li  P  tan- 
gent  to  i)othtlie  n»oon  and  the  sun,  but  crossing  each  other 
between  these  bodies  at  h.  It  is  evident  that  outside  the 
space  P  li  B'  P'  an  observer  will  see  the  whole  sun,  no 
part  of  the  m(x»n  being  projected  ujwn  it ;  while  within 
this  space  the  sun  will  be  more  or  less  obscured.  The 
whole  obscured  space  may  bo  divided  into  three  regiotis,  in 
each  of  which  the  character  of  the  phenomenon  is  differ- 
ent from  what  it  is  in  the  others. 

Firstly,  we  have  the  region  B  VB'  fonning  the  shadow 
cone  proper.  Here  the  sunlight  is  entirely  cut  off  by  the 
moon,  and  darkness  is  therefore  complete,  except  so  far  as 
light  may  enter  by  refraction  or  reflection.  To  an  observer 
at  V  the  moon  would  exactly  cover  the  sun,  the  two 
bodies  being  apparently  tangent  to  each  other  all  around. 

Secondly,  we  have  the  conical  region  to  the  right  of  V 
between  the  lines  B  Fand  B'  V  continued.  In  this 
region  the  moon  is  seen  wholly  projected  upon  the  sun, 
the  visible  portion  of  the  latter  presenting  the  form  of  a 
ring  of  light  around  the  moon.  This  ring  of  light  will  be 
wider  in  proportion  to  the  apparent  diameter  of  the  sun, 
the  farther  out  we  go,  because  the  moon  will  appear 
smaller  than  the  sun,  and  its  angular  diameter  will  dimin- 
ish in  a  more  rapid  ratio  than  that  of  the  sun.  This 
region  is  that  of  annular  eclipse,  because  the  sun  will  pre- 
sent the  appearance  of  an  annulus  or  ring  of  light  around 

the  moon. 

Thirdly,  we  have  the  region  PB  VandP'B  V,  which 
we  notice  is  connected,  extending  around  the  interior  cone. 
An  observer  hero  would  see  the  moon  partly  projected 
upon  the  sun,  and  therefore  a  certain  part  of  the  sun's 
light  would  be  cut  off.  Along  the  inner  boundary  B  V 
and  B'  V  the  obscuration  of  the  sun  will  be  complete, 
but  the  amount  of  sunlight  will  gradually  increase  out  to 


174 


AtiTRONOMY. 


tliu  outer  boiimlary  B  /'  Ji'  7",  wliorc  tlio  whole  sun  is 
vi8il>lu.  This  region  uf  pai-'jiil  obseuration  is  culluil  the 
jtcnumbra. 

To  sliow  more  clearly  t'iic  phenomena  of  solar  c('li|iHo, 
we  jircseiit  another  figure  reprcsi-iiting  the  pentimhra  of 


Fio.  fll.— noiTRB  or  hhadow  por  MxnvhAit  bclifbb. 

tlie  moon  tlirown  upon  the  earth.*  The  outer  of  the  two 
circles  S  represents  the  limb  of  the  sun.  The  exterior  tan- 
gents which  mark  the  boundary  of  the  shadow  cross  each 
other  at  F  before  reaching  the  earth.  The  earth  being 
a  little  beyond  the  vertex  of  the  shadow,  there  can  be  no 
total  ccli^)se.  In  this  case  an  observer  in  the  penumbral 
region,  C  0  or  D  Oy  will  see  the  moon  partly  projected  on 
the  sun,  v/hile  if  ho  chance  to  be  sitnated  at  O  he  will  see 
an  annular  eclipse.  To  show  how  this  is,  we  draw  dotted 
lines  from  O  tangent  to  the  moon.  The  angle  bolAoen 
these  lines  represents  the  apparent  diameter  of  the  moon 
as  seen  from  the  earth.  Continuing  them  to  the  sun,  they 
show  the  apparent  diameter  of  the  moon  as  projected  upon 
the  sun.     It  will  be  seen  that  in  the  case  supposed,  when 


*  Tt  will  In;  noted  that  nil  the  HgiircH  of  eclipses  nrc  necessarily  drawn 
very  much  out  of  proportion.    Really  the  sun  is  400  times  the  distance 
of  the  moon,  whicli  again  is  00  times  the  radius  of  the  earth.     But  it 
would  lie  entirely  impossible  to  draw  a  figure  of  this  proportion  ;  wi 
are  therefore  obliged  to  represent  the  earth  as  larger  than  the  sun,  ani 
the  moon  as  nearly  half  way  between  the  earth  and  sun. 


th 
th 
th 
sic 

rei 


in 
ec 


ili.lJia*iHiM.j.i|IIA<  I 


~Z}. 


O    8UT1  IB 

tllud  the 

•  C('li|)HO. 
iuil>ra  uf 


E0LIP8B8  OF  TUh'  HUN. 


175 


the  vortex  of  the  shadow  is  hotweon  the  earth  and  moon, 
tlie  hitter  will  neccHsarily  apjHjar  sniallcr  tlian  the  rjui,  and 
the  observer  will  see  a  portion  of  the  solar  disk  on  all 
sides  of  the  moon,  as  shown  in  Fig.  (52. 

If  the  moon  were  a  little  nearer  the  eaith  than  it  is  rep- 
resented in  the  figure,  its  shadow  would  reach  the  earth 


nn. 

>f  the  two 
ten  or  tan- 
cross  each 
firth  being 
can  be  no 
pcnumbral 
ojected  on 
[le  will  see 
•aw  dotted 
i  bfct*veen 
the  moon 
5  sun, they 
icted  upon 
ised,  when 

iHarily  drawn 
the  distance 
kfth.  But  it 
portion ;  we 
the  sun,  and 


FlO.  62.— DARK    BOOT    OF   MOON  nUMECTBD  OH  SUN  DORINU  AN 
ANNOLAR  ECLIP8B. 

in  the  neighljorhood  of  O.  We  should  then  liave  a  total 
eclipse  at  each  point  of  the  earth  on  which  it  fell.  It  will 
be  seen,  however,  that  a  total  or  annular  eclipse  of  the  sun 
is  visible  only  on  a  very  small  portion  of  the  earth's  sur- 
face, because  the  distance  of  the  moon  changes  so  little 
that  the  earth  can  never  be  far  from  the  vertex  Fof  the 
shadow.  As  the  moon  moves  around  the  earth  fi-om  west 
to  east,  its  shadow,  wliether  the  eclipse  be  total  or  annu- 
lar, moves  in  the  same  direction.  The  diameter  of  the 
shadow  at  the  surface  of  the  earth  ranges  from  zero  to  150 
miles.  It  therefore  sweeps  along  a  belt  of  the  earth's  sur- 
face of  that  breadth,  in  the  same  direction  in  which  the 
<jartli  is  rotating.  The  velocity  of  the  moon  relative  to 
the  earth  being  3400  kilometres  per  hour,  the  shadow 
would  pass  along  with  this  velocity  if  the  earth  did  not  ro- 
tate, but  owing  to  the  earth's  rotation  the  velocity  rektive 


176 


AtiTliUiSOM  Y. 


to  |H»int«  on   itH  Hiirftwo  riiiiy  raiif^c   from  2000  to  3400 
kiloMictivH  (1200  to  2100  mih'H). 

The  ruiuler  will  readily  umlc!r«tiiiKl  tliiit  in  (trder  to  hoc 
a  total  wlipHU  an  olmciver  iiiUHt  station  liin»»ell'  hcforo- 
haiid  at  m\\w  point  of  the  carth'H  HuriWo  over  which  the 
Hhadow  is  to  paHH.  These  points  ai-e  ^'enerally  ealr,ulate»l 
Home  years  in  ailvanee,  in  the  iwtronomieal  ephemerides, 
with  as  inueh  precision  as  the  tables  of  the  celestial  mo- 
tions admit  of. 

It  will  ho  seen  that  a  partial  eclipse  of  the  sun  may  Im) 
visible  from  a  much  larger  jwrtioii  of  the  earth's  surfaco 
than  a  tt>tal  or  annular  one.  The  space  CD  (Kig.  «!)  over 
^vhi(;h  the  penumbra  extends  is  generally  of  about  one  hull 
the  diameter  of  the  earth.  Roughly  speaking,  a  partni! 
eelipso  of  the  su);  may  sweep  over  a  ]M>rtion  of  the  earth's 
surface  ranging  from  zero  to  perhaps  one  fifth  or  one  sixth 

of  the  whole. 

There  are  really  more  eclipses  of  the  eun  than  «)f  tlie 
moon.     A  year  never  passes  without  at  least  two  of  the 
fonner,  and  sometimes  five  or  six,  while  there  are  rarely 
mon  than  two  eclipses  of  the  moon,  an«l  in  many  years 
now:  ;Af  all.    But  at  any  one  place  more  eclipses  of  the  moon 
vill  ,c  seen  than  of  the  sun.     The  reason  of  this  is  that 
an  eclipse  of  the  moon  is  visible  over  the  entire  hemi- 
sphere of  the  earth  on  which  the  moon  is  shining,  and  aa  it 
lasts  several  hours,  observers  who  are  not  in  this  hemi- 
sphere at  the  beginning  of  the  eclipse  may,  by  the  earth's  i-o- 
tation,  be  brought  into  it  before  it  ends.    Thus  the  eclipse 
will  be  seen  over  more  than  half  the  earth's  surface.    But, 
as  we  have  just  seen,  each  eclipse  of  the  sun  can  be  seen 
over  oidy  so  small  a  fraction  of  the  earth's  surface  as  to 
more  than  compensate  for  the  greater  absolute  frequency 
of  solar  eclipses. 

It  will  be  seen  that  in  order  to  have  either  a  total  or  ari«^ 
nular  eclipse  visible  upon  the  earth,  the  line  joining  the 
centres  of    the  sun  and    moon,  being  continued,  must 
strike  the  earth.     To  an  observer  on  this  line,  the  centres 


>il_ 


to  3400 

ler  to  Hcc 
I'  hcforo- 
vliich  tliu 

'illcllliltctl 

,!ineri(loH, 
Htial  ino- 


f^ 


■2 


w  may  bo 
'h  Hurfttco 
,  ISl)  over 
t  onu  liuit' 

u  parttu) 
lio  eartli'^ 

une  eixth 

lan  of  tlic 
wo  of  the 
are  rarely 
lany  years 
:  the  moon 
^hig  is  that 
tiro  hemi- 
r,  and  as  it 
this  heini- 
earth'sro- 
tho  eclipse 
face.    But, 
;an  be  seen 
irfaco  as  to 
!  frequency 

total  or  art*-' 
joining  the 
lued,  must 
the  centres 


i^igjjaftiouaiiawm 


^em^^m^mymMMuj..'-^.-^-  f>#''rm->f.^.-,'f..^^.,Ai..m  L.i'i^.:.  .r,... .,).  .■r;?'g^'tP#H!#Piy'^S^''"' 


._J 


CIHM/ICMH 


Series. 


CIHM/ICMH 
Collection  de 
microfiches. 


Canadian  Instituta  for  HIatorical  Microraproductiona  /  Inatftut  Canadian  da  microraproductiona  hiatoriquaa 


BEGURRENOK  OF  EGLlPSBa. 


177 


of  the  two  bodies  will  seem  to  coincide.  An  eclipse  in 
which  this  occurs  is  called  a  central  one,  whether  it  be 
total  or  annular.  The  accompanying  figure  will  perhajis 
aid  in  giving  a  clear  idea  of  the  plienoinena  of  eclipses  of 
both  sun  and  moon. 


FlO.  63.^COMPARI80N  OV  SHADOW  AND  PKNimBRA  OF  EARTH  AKD 
MOON.  A  IS  THE  POSITION  OP  TUB  MOON  DUBINO  A  BOLAK,  B  DCB- 
INO  A  LUNAR  ECLIPSE. 

§  4.    THX  BXOUBBHNCE  OF  aOUPSES. 

If  the  orbit  of  the  moon  around  the  earth  were  in  or 
near  the  same  plane  with  that  of  the  latter  around  the  sun 
— that  is,  in  or  near  the  plane  of  the  ecliptic — It  will  be 
readily  seen  that  there  would  be  an  eclipse  of  the  sun  at 
every  new  moon,  and  an  eclipse  of  the  moon  at  every 
full  moon.  But  owing  to  the  inchnation  of  the  moon's 
orbit,  described  in  the  last  chapter,  the  shadow  and 
penumbra  of  the  moon  commonly  pass  above  or  below  the 
earth  at  the  time  of  new  moon,  while  the  moon,  at  her 
full,  commonly  passes  above  or  below  the  shadow  of  the 
earth.  It  is  only  when  at  the  moment  of  new  or  full  moon 
the  moon  is  near  its  node  that  an  eclipse  can  occur. 

The  question  now  arises,  how  near  must  the  moon  be  to 
its  node  in  order  that  an  eclipse  may  occur  ?  It  is  found 
by  a  trigonometrical  computation  that  if,  at  the  moment 
of  new  moon,  the  moon  is  more  than  18° '6  from  its 
node,  no  eclipse  of  the  sun  is  possible,  while  if  it  is  less 
&aa  18**  •  7  an  eclipse  is  certain.  Between  these  limits  an 
ecUpse  auLj  occur  or  fail  aocording  to  the  respeotiye  dis- 
taaocB  of  tiie  snn  and  moon  from  tibe  earth.  Half  way  be- 
tw«en  these  limits,  or  say  16**  from  the  node,  it  is  an  even 


y 


IW 


ASTRONOMY. 


uhance  that  an  eclipBe  will  occur ;  toward  the  lower  limit 
(13° -7)  the  chances  increase  to  certainty;  toward  the 
upper  one  (18°  •  6)  they  diminish  to  zero.  The  correspond- 
ing limits  for  an  eclipse  of  the  moon  are  9°  and  12^° — that 
is,  if  at  the  moment  of  full  moon  the  distance  of  the 
moon  from  her  node  is  greater  than  Vi^^  no  eclipse  can 
occur,  while  if  the  distance  is  less  than  9°  an  eclipse  is  cer- 
tain. Wo  may  put  the  mean  limit  at  11°.  Since,  in  the 
long  run,  new  and  full  moon  will  occur  equally  at  all  dis- 
tances from  the  node,  there  will  be,  on  the  average,  sixteen 
eclipses  of  the  sun  to  eleven  of  the  moon,  or  nearly  fifty  per 
cent  more. 


Fra.  64.— mutntias  Imiar  cdipM  at  diUMeiit  dMuow  ftrom  ttw  nod*.  The  dark 
circle*  ar«  Ike  earth's  ahadow,  tiia  ceatre  of  whieh  Is  alwajrs  in  the  ecliptie  AB.  The 
moon's  orbit  is  represented  ^jOD.  At  (3>  the  eelipso  is  central  and  total,  at  J'Uls 
partial,  and  at  K  there  is  baieljr  an  ecUpse. 

tut  an  illustration  of  these  computatioiM,  let  us  investigatQ  the  lim- 
its within  which  a  central  eclipse  of  the  sun^  total  or  annular,  can 
occur.  To  allow  of  such  an  eclipse,  it  is  oTident,  from  an  inspec- 
tion of  Fig.  61  or  68  that  the  actual  distance  of  the  moon  from 
the  plane  of  the  ecliptic  must  be  less  than  the  earth's  racUus, 
because  the  line  joining  the  centres  of  the  sun  and  earth  always  lies 
in  this  plane.  This  distance  must,  therefore,  be  leaa  than  6870  kilo- 
m«trea-  The  mean  distance  of  the  moon  being  884,000  kilometres, 
the  sine  of  the  latitude  at  this  limit  is  jfUHi  mi<1  ^^  Utitude  itself 
is  57'.    The  formula  for  the  latitude  u,  by  sjdwrical  trigonometry, 

rin  latitude  =  sin  •  sin  «, 

» being  the  inclination  of  the  moon's  orbit  (5*  80,  ud  « the  distance 
of  the  moon  from  the  node.  The  value  of  sin  <  is  ncA  far  fmn  A. 
while,  in  a  rough  calcuhtion,  we  may  suppose  the  comnaratively 
small  angles  «  and  the  latitude  to  be  tlM  mow  as  theb  miiQs.  We 
may,  therefore,  suppose 

tt=rll  latitDdesB  t^'. 


BEVURttENOE  OF  ECLIPSES. 


179 


ird  the  lower  limit 
iinty ;  toward  thu 

The  correspond- 
9"  and  12^°— that 
[6  distance  of  the 
2^**  no  eclipse  can 

an  eclipse  is  oer- 
1°.     Since,  in  the 

equally  at  all  dis- 
he  average,  sixteen 
I,  or  nearly  fifty  per 


■  fhmittMiiod*.  Tiiedirk 
jrt  In  the  ecllptie  AB.  Ttta 
OMUml  andtoUl,  at  JTUU 


ua  invettigatQ  the  lim- 
,  total  or  wmular,  can 
idnit,  from  an  iii8pec> 
Be  of  the  moon  Iram 
a  the  earth's  radius, 
I  and  earth  always  lies 
te  less  than  «870]dlo- 
ig  884,000  kilometns, 
and  the  latitude  itself 
iherical  trigonometry, 

h 

80,  and  « the  distance 
a  <  is  not  far  f mn  A, 
MS  the  ooapnntiTely 
e  as  their  uaes.    We 


We  therefore  conclude  that  if,  at  the  moment  of  new  moon,  the 
distance  of  the  moon  from  the  node  is  less  than  101°  there  will  be 
a  central  eclipsr,  of  the  sun,  and  if  greater  than  this  there  will  not  be 
such  an  •«lip«o.  The  eclipse  limit  may  range  half  a  degree  or  more 
on  each  side  of  this  mean  value,  owing  to  the  varying  distance  of 
the  moon  from  the  earth.  Inside  cf  10  a  central  eclipse  may  be  re- 
garded as  certain,  and  outside  of  11°  as  impossible. 


If  the  direction  of  the  moon's  nodes  from  the  centre  of 
the  earth  were  invariable,  eclipses  could  occur  only  at  the 
two  opposite  months  of  tlie  year  when  the  sun  had  nearly 
the  same  longitude  as  one  node.  For  instance,  if  the  lon- 
gitudes of  the  two  opposite  nodes  were  respectively  54'^ 
and  234°,  then,  since  the  sun  must  be  within  12°  of  the 
node  to  allow  of  an  eclipse  of  the  moon,  its  longitude 
would  have  to  be  either  between  42°  and  66°,  or  between 
222°  and  246°.  But  the  sun  is  within  the  first  of  these  re- 
gions only  in  the  month  of  May,  and  within  the  second  only 
during  the  month  of  November.  Hence  lunar  eclipses 
could  then  occur  only  during  the  months  of  May  and  No- 
vember, and  the  same  would  hold  true  of  central  eclipses 
of  the  sun.  Small  partial  eclipses  of  the  latter  might  be 
seen  occasionally  a  day  or  two  from  the  beginnings  or  ends 
of  the  above  months,  but  they  would  be  very  small  and 
quite  rare.  Now,  the  nodes  o "  the  moon's  orbit  were  act- 
ually in  the  above  directions  in  the  year  1873.  Hence 
during  that  year  eclipses  occurred  only  in  May  and  No- 
vember. We  may  call  these  months  the  seasons  of  eclipses 
for  1873. 

But  it  was  explained  in  the  last  chapter  that  there  is  a 
refaoigrade  motion  of  the  moon's  nodes  amounting  to  19^° 
in  a  year.  The  nodes  thus  move  back  to  meet  the  sun  in 
its  annual  revolution,  and  th  meeting  occurs  about  20  days 
eariiw  every  year  than  it  did  the  year  before.  The  re- 
salt  is  that  tibe  season  of  eclipses  is  constantly  shifting,  so 
that  each  season  ranges  throngfaout  the'whole  year  in  18*6 
yean.  Tor  instance,  the  season  oorreeponding  to  that  of 
November,  1873,  had  moved  baok  to  July  and  August  in 


180 


ASTRONOMY. 


1878,  and  will  wicur  in  May,  1882,  while  that  of  May, 
1873,  will  bo  shifting  back  to  November  in  1882. 

It  may  bo  intoreBting  to  illuBti-ato  this  by  giving  the 
days  in  which  the  sun  is  in  conjunction  with  the  nodes  of 
the  moon's  orbit  during  several  years. 


AKCuding  Node. 

1879.  January  24. 

1880.  January  6. 

1880.  December  18. 

1881.  November  30. 

1882.  November  12. 

1883.  October  25. 

1884.  Octobers. 


DeiicondlDg  Mode. 

1879.  July  17. 

1880.  Jime27. 

1881.  June    8. 

1882.  May  20. 

1883.  May    1. 

1884.  April  12. 

1885.  March  25. 


During  these  years,  eclipses  of  the  moon  can  occur  only 
within  11  or  12  days  of  these  dates,  and  eclipses  of  the 
sun  only  within  15  or  16  days. 

In  consequence  of  the  motion  of  the  moon's  node,  three 
varying  angles  come  into  play  in  considering  the  occur- 
rence of  an  eclipse,  the  longitude  of  the  node,  that  of  the 
sun,  and  that  of  the  moon.  We  may,  however,  simplify 
the  matter  by  referring  the  directions  of  the  sun  and 
moon,  not  to  any  fixed  line,  but  to  the  node — t&at  is,  we 
may  count  the  longitudes  of  these  bodies  from  the  node 
instead  of  from  the  vernal  equinox.  We  have  seen  in  the 
last  chapter  that  one  revolution  of  the  moon  relatively  to 
the  node  is  accomplished,  on  the  average,  in  27  •  21222 
days.  If  we  calculate  the  time  required  for  the  sun  to  re- 
turn to  the  node,  we  shall  find  it  to  be  346  •  6201  days. 

Now,  let  US  suppose  the  sun  and  moon  to  start  out 
together  from  a  node.  At  the  end  of  346 '6201  days  the 
sun,  having  apparently  performed  nearly  an  entire  rev- 
olution around  the  celestial  sphere,  will  again  be  at  the 
same  node,  which  has  moved  back  to  meet  it.  But  the 
moon  will  not  be  there.  It  will,  during  the  interval,  have 
passed  the  node  12  times,  and  the  18th  paasage  will  not 
occur  for  a  week.    The  same  thing  will  be  tme  for 


BECUBRENVB  OF  ECL/P8E8. 


181 


ilo  that  of  May, 

ill  1882. 

lis  by  giving  tho 

iritli  tlio  nodes  of 

mdlng  Node. 

July  17. 
June  27. 
June    8. 
May  20. 
May    1. 
April  12. 
Marcli  25. 

in  can  occur  oitly 
1  eclipses  of  tho 

oon's  node,  three 
lering  the  occur- 
node,  that  of  the 
lowever,  simplify 
of  the  sun  and 
lode — that  is,  we 
fl  from  the  node 
have  seen  in  the 
loon  relatively  to 
ige,  in  27-21222 
for  the  sun  to  re- 
^•6201  days. 
lOon  to  start  out 
16-6201  days  the 
y  an  entire  rev- 
i  again  be  at  the 
leet  it.  But  the 
he  interval,  have 
paamge  will  not 
lill  be  true  for 


IS  successive  returns  of  the  sun  to  the  node ;  we  shall 
not  lind  the  moon  there  at  the  same  time  with  the  sun  ; 
she  will  always  have  passed  a  little  sooner  or  a  little  later. 
But  at  the  10th  return  of  the  sun  and  the  24:2d  of  the 
moon,  the  two  bodies  will  be  in  conjunction  within  half 
a  degree  of  the  node.  Wo  iind  from  the  preceding 
periods  that 

242  returns  of  the  moon  to  the  node  require  6585  -  357  days. 

19       ♦'         "      sun     "         "        "  6585-780   " 

The  two  IxMlies  will  therefore  pass  the  node  within  10 
hours  of  each  other.  This  conjunction  of  the  sun  and 
moon  will  be  the  223d  new  moon  after  that  from  which 
wo  started.  Now,  one  lunation  (that  is,  the  interval 
between  two  consecutive  new  moons)  is,  in  the  mean, 
29-530588  days  ;  223  lunations  therefore  require  6585-32 
days.  The  new  moon,  therefore,  occurs  a  little  before  the 
bodies  reach  the  node,  the  distance  from  the  latter  being 
that  over  which  the  moon  moves  in  0*-036,  or  the  sun  in 
0^-i59.  We  readily  find  this  distance  to  be  28' of  arc, 
somewhat  less  than  the  apparent  semidiameter  of  either 
body.  This  would  be  the  smallest  distance  from  either 
node  at  which  any  new  moon  would  occur  during  the 
whole  period.  The  next  nearest  approaches  would  have 
occurred  at  the  35th  and  47th  lunations  respectively. 
The  36th  new  moon  would  have  occurred  about  6°  before 
the  two  bodies  arrived  at  the  node  from  which  we  started, 
and  the  47th  about  1^°  past  the  opposite  node.  No  other 
new  moon  would  occur  so  near  a  node  before  the  223d 
one,  which,  as  we  have  just  seen,  would  occur  0"  28' 
west  of  the  node.  This  period  of  223  new  moons,  or  18 
years  11  days,  was  called  the  Saras  by  the  ancient  astron- 
omers. 

It  will  be  seen  that  in  the  preoedinff  calcnlalioiu  we  taftre  aMumed 
the  ran  aad  moon  to  more  uniformly,  so  that  the  aucceuive  new 
moon's  occurred  at  equal  intervals  of  29 -680588  days,  and  at  equal 
angular  distances  around  the  ecliptic.  In  fact,  however,  the  month- 
ly uuqnslities  in  the  motioa  at  the  moon  cause  deviatiomi  from  lier 


182 


AaTRONOMY. 


% 


mean  motion  which  amount  to  six  doffroei  in  either  direction,  while 
the  annual  inequality  in  the  motion  of  the  sun  in  lonsitiide  is  nearly 
two  degrees.  Consequently,  our  conclusions  respecting  the  point  at 
which  new  moon  occurs  may  be  astray  by  eight  degrees,  owing  to 
these  inequalities. 

But  there  is  a  remarkable  feature  connected  with  the  Saros  which 
greatly  reduces  these  inequalities.  It  is  that  this  period  of  6585} 
days  corresponds  very  nearly  to  an  integral  number  of  revolutions 
both  of  the  eartli  round  the  sun,  and  of  the  lunar  perigee  around 
the  earth.  Hence  the  inequalities  both  of  the  moon  and  of  the 
sun  will  be  nearly  the  same  at  the  beginning  and  the  end  of  a  Saros. 
In  fact,  ttSSfil  days  is  about  18  years  and  11  days,  in  which  time 
the  earth  will  have  made  18  revolutions,  and  about  11°  on  the 
10th  revolution.  The  longitude  of  the  sun  will  therefore  be  about 
11°  greater  than  at  the  Mginning  of  the  period.  Again,  in  the 
same  perio<l  the  moon's  perigee  will  have  made  two  revolutions, 
and  will  have  advanced  18°  88'  on  the  third  revolution.  The  sun 
and  moon  being  11°  further  advanced  in  longitude,  the  conjunction 
will  fall  at  the  same  distance  from  the  lunar  perigee  within  two  or 
three  degrees.  Without  going  through  the  details  of  the  calcula- 
tion, we  uiay  say  as  the  result  of  this  remarkable  coincidence  that 
the  time  of  the  228d  lunation  will  not  generally  be  accelerated  or 
retarded  more  than  half  an  hour,  thou^  those  of  the  intermediate 
lunations  will  sometimes  deviate  more  than  half  a  day.  Also  that 
the  distance  west  of  the  node  at  which  the  new  moon  occurs  will 
not  generally  differ  from  its  mean  value,  28'  by  more  than  20'. 


In  the  preceding  explanation,  we  have  eapposed  the  snn 
and  moon  to  start  ont  together  from  one  of  the  nodes  of 
the  moon^s  orbit.  It  is  evident,  however,  that  we  might 
have  supposed  them  to  start  from  any  given  distance  east 
or  west  of  the  node,  and  should  then  at  the  end  of  the  223d 
lunation  find  them  together  again  at  nearly  that  distance 
from  the  node.  For  instance,  on  the  6th  day  of  May, 
1864,  at  seven  o'clock  in  the  evening,  Washington  time, 
new  moon  occurred  with  the  sun  and  moon  2°  26'  west  of 
the  descending  node  of  the  moon's  orbit.  Counting  for- 
ward 223  lunations,  we  arrive  at  the  16th  day  of  May, 
1882,  when  we  find  the  new  moon  to  occur  3°  20'  west  of 
the  same  node.  Since  the  character  of  the  eclipse  depends 
principally  upon  the  relative  position  of  the  sun,  the  moon, 
and  the  node,  the  result  to  which  we  are  led  may  be  stated 
as  follows : 

Let  us  note  the  time  of  the  middle  of  any  eclipse. 


RKVURRBNGB  OF  B0LIP8B8. 


188 


either  diroction,  while 
I  in  lonffitude  is  nearly 
respecting  the  point  at 
ght  degrees,  owing  to 

with  the  Saros  which 
t  this  period  of  658S1 
number  of  revolutions 

lunar  perigee  around 
the  moon  and  of  the 
md  the  end  of  a  Saros. 

days,  in  which  time 
and  about  11°  on  the 
rill  therefore  be  about 
leriod.  Again,  in  the 
nade  two  revolutions, 

revolution.  The  sun 
itttde,  the  conjunction 
perigee  within  two  or 
oetaiTs  of  the  calcula- 
kable  coincidence  that 
rally  be  accelerated  or 
ose  of  the  intermediate 
half  u  day.  Also  that 
new  moon  occurs  will 
by  more  than  30'. 

ve  supposed  the  snn 
)ne  of  the  nodes  of 
ever,  that  we  might 
given  distance  east 
theendof  the22dd 
learly  that  distance 
B  5th  day  of  May, 
,  Washington  time, 
noon  S**  35'  west  of 
'bit.  Counting  for- 
16th  day  of  Hay, 
>ccur  3°  20'  west  of 
'  the  eclipse  depends 
the  sun,  the  moon, 
«  led  may  be  stated 

die  of  any  eclipse. 


whotlior  of  the  buii  or  of  the  moon.  Tliuii  let  lis  go  for- 
ward 0585  dayu,  7  hours,  42  minuluH,  nnd  wo  shall  find 
unothor  cclipsu  very  Hiniilar  to  the  tirst.  Iludnced  to  years, 
the  interval  will  be  18  years  and  10  or  11  days,  according 
as  a  2Utli  day  of  February  intervenes  four  or  live  times 
during  the  interval.  This  Iwing  true  of  every  eclipse,  it 
follows  that  if  we  record  all  the  eclipses  which  occur  dur- 
ing a  ])eriod  of  18  years,  we  shall  find  a  new  set  to  begin 
over  again.  If  the  period  were  an  integral  number  of 
(lays,  each  eclipse  of  the  new  set  would  be  visible  in  the 
same  regions  of  the  earth  as  the  old  one,  but  since  there  is 
a  fraction  of  nearly  8  hours  over  the  round  imniber  of 
days,  the  earth  will  be  one  third  of  a  revolution  further 
advanced  before  any  eclipse  of  the  new  set  begins.  Each 
eclipse  of  the  new  set  will  therefore  occur  about  one  third 
of  the  way  round  the  world,  or  120°  in  longitude  west  of 
the  region  in  which  the  old  one  occurred.  The  recur- 
rence will  not  take  place  near  the  same  region  until  the  end 
of  three  periods,  or  54yeanB ;  and  then,  since  there  is  a 
slight  deviation  in  the  series,  owing  to  each  new  or  full 
moon  occurring  a  little  further  west  from  the  node,  the 
fourth  eclipse,  though  near  the  same  region,  will  not 
necessarily  be  similar  in  all  its  particulars.  For  example, 
if  it  be  a  total  eclipse  of  the  sun,  the  path  of  the  shadow 
may  be  a  thousand  miles  distant  from  the  path  of  54  years 
previously. 

As  a  recent  example  of  the  Saros,  we  may  cite  some 
total  eclipses  of  the  '  '.*  well  known  in  recent  times  ;  for 
instance : 

1842,  July  8th,  l**  a.m.,  total  eclipse  observed  in 
Europe ; 

1860,  July  18th,  9^  a.m.,  total  eclipse  in,  America  and 
Spain ; 

1878,  Jnly  39th,  4^  p.m.,  one  visible  in  Texas,  Col- 
orado, and  on  the  coast  of  Alaska. 

A  yet  more  reuuurkable  series  of  total  edipsee  of  the 


184 


AStTttONOMT. 


mn  uro  those  of  thoyeiirB  1850,  1808,  188<),  utc,  tho  dates 
and  regions  1)eing : 

1850,  August  7tli,  4''  I'.M.,  in  tlie  Pacific  Ocean  ; 

18«8,  August  17tli,  12''  I'.M.,  in  India; 

1880,  August   2»th,  8''   a.m.,  in   tho  Central    Atlantic 
<  )cean  and  Southern  Africa  ; 

iyo4,  Septeud)er  Uth,  noon,  in  South  America. 

This  scries  is  remarkable  for  the  long  duration  of  total- 
ity, aiaouuting  to  some  six  minutes. 

Let  lis  now  consider  a  series  of  ecliiHies  recurring  at  i-eg- 
ular  intervals  of  18  years  and  11  days.     Since  every  suc- 
cessive recurrence  of  such  an  eclipse  throws  the  conjunc- 
tion 28'  further  toward  tho  west  of  the  node,  the  conjunc- 
tion must,  in  process  of  time,  take  place  so  far  back  from 
tho  node  that  no  eclipse  will  occur,  and  the  series  will  end. 
For  the  same  reason  there  must  be  a  commencement  to 
the  series,  the  first  eclipse  being  east  of  the  node.    A  new 
eclijjse  thus  entering  will  at  first  be  a  very  small  one,  but 
will  be  larger  at  every  recurrence  in  each  Saros.     If  it  is 
an  eclipse  of  the  moon,  it  will  be  total  from  its  18th  until 
its  36th  recurrence.     There  will  then  be  about  18  partial 
eclipses,  each  of  which  will  bo  smaller  than  the  kst,  when 
they  will  fail  entirely,  the  conjunction  taking  place  so  far 
from  the  node  that  the  moon  does  not  touch  the  earth's 
shadow.     The  whole  interval  of  time  over  which  a  series 
of  lunar  eclipBCS  thus  extend  will  be  about  48  periods,  or 
865  years. 

When  a  series  of  solar  eclipses  begins,  the  penumbra  of 
the  finst  will  just  graze  the  earth  not  far  from  one  of  the 
poles.  There  will  then  be,  on  the  average,  1 1  or  12  partial 
eclipses  of  the  sun,  each  lai^r  than  the  preceding  one, 
occurring  at  regular  intervals  of  one  Saros.  Then  the 
central  line,  whether  it  be  that  of  a  total  or  annular 
eclipse,  will  begin  to  touch  the  earth,  and  we  shall  have  a 
series  of  40  or  50  central  edipBes.  The  central  line  will 
strike  near  one  pole  in  the  first  part  of  the  MRW ;  in  the 
equatorial  regions  about  the  middle  of  tlie  aoriet,  Mid  will 


VtlAUAGTKIlH  OF  MHJI'SKS. 


185 


SB,  utc,  thu  datu8 

itic  Ocuuii  ; 

Ouiitrul    Atliiiitic 

Aiiiurica. 
durutiun  uf  tuta]- 

i  rufurriiig  at  ivg- 
8incti  every  buc- 
row8  the  coiijuuu- 
tude,  the  coiiji.iic- 
)  so  far  back  from 
he  8erio8  will  end. 
ioinmeucemeiit  to 
the  node.  A  new 
cry  gniall  one,  but 
ch  Sarofl.  If  it  is 
^rom  its  13th  until 
10  about  18  partial 
ban  the  last,  when 
Aking  place  so  far 
touch  the  earth's 
iver  which  a  series 
>out  48  periods,  or 

,  the  penumbra  of 
■  from  one  of  the 
^,  llor  12  partial 
he  preceding  one, 
Sarofl.  Then  the 
I  total  or  annular 
nd  we  shall  have  a 
e  centra]  line  will 
theMrifls;  in  the 
diesMMs,  Mid  will 


Icuvu  the  earth  by  thu  other  ]k)Iu  ut  the  end.  Tun  or 
twulvu  partial  u(!li|MuM  will  follow,  and  this  particular  ite- 
rics  will  cuHHu.  Tliu  wbolu  iiuinbur  in  the  series  will  avur- 
age  iHitwuun  00  und  7U,  occupying  u  fuw  uenturies  over  a 
thoiiHiuid  years. 

$(  6.    0HABA0TBB8  OF  B0LIP8B8. 

Wc  have  seen  that  tho  |ioMibility  of  a  tutal  eclipso  of  the  sun 
iiriaeH  from  the  occaHional  very  Hiight  excesa  of  tho  apparent  anaular 
diameter  of  the  moon  over  that  of  the  sun.  This  excess  is  so  slight 
that  such  an  eclipse  can  never  last  more  than  a  few  minutes.  It 
may  be  of  interest  to  point  out  the  circumstances  which  favor  a 
long  duration  of  totality.    These  are : 

(1)  That  the  moon  should  be  as  near  as  possible  to  the  earth,  or, 
technically  speaking,  in  perigee,  because  Its  angular  diameter  as 
Hccn  from  the  earth  will  then  be  greatest. 

(2)  That  the  sun  should  be  near  its  greatest  distance  from  the 
earth,  or  in  apogee,  because  then  its  angular  diameter  will  be  the 
least.  It  is  now  in  this  position  about  tne  end  of  June  ;  hence  the 
most  favorable  time  for  a  total  eclipse  of  very  long  duration  is  in 
the  summer  months.  Since  the  moon  must  bo  in  perioee  and  alao 
between  the  earth  and  aun,  it  follows  that  the  longitude  of  the 
perigee  must  be  nearly  that  of  the  sun.  Hie  longitude  of  the  sun 
at  the  end  of  June  Iwing  100*,  thia  is  the  most  favorable  longi- 
tude of  the  moon's  perig«e. 

(8)  The  moon  must  m  very  near  the  node  in  order  that  the  cen- 
tre of  the  shadow  may  fall  near  the  equator.  The  reason  of  this  con- 
dition is,  that  the  duration  of  a  total  eclipse  may  be  oonaidenibly 
increased  by  the  rotation  of  the  earth  on  ita  azia.  We  have  seen 
that  the  shadow  sweeps  over  the  earth  from  west  toward  east  with  a 
velocity  of  about  8400  kilometres  per  hour.  Since  the  earth  rotates  in 
the  same  direction,  the  velocity  relative  to  the  observer  on  the  earth's 
surface  will  be  diminished  by  a  quantity  depending  on  thia  velocity 
of  rotation,  and  therefore  greater,  the  greater  t&  velocity.  Tb« 
vebMsity  of  rotation  u  greatest  at  the  earth's  equator,  when  it 
amounts  to  1600  kibtowtres  per  hour,  or  nearly  half  the  velocity  of 
the  moon's  shadow.  Hence  tne  duration  of  a  total  ecline  may,  with- 
in the  tropics,  be  nearly  doubled  bvthe  earth's  rot^ion.  when  all 
the  favorable  cireumstances  comUne  in  the  way  we  have  just  de- 
scribed, the  duration  of  a  total  eclipse  within  the  tropica  will  be 
about  seven  minutes  and  a  half.  In  our  latitude  thrmudmum  du- 
rati<m  will  be  somewhat  less,  or  not  far  from  six  minutea,  but  it  is 
only  on  vety  ran  ooeaaiona,  hardly  once  in  many  centuries,  that  all 
these  faveirable  conditioas  can  be  expected  to  coticur. 

Of  late  yean,  solar  eclipMS  have  derived  an  inoreaied  in- 
terest from  the  faet  that  during  the  few  minutes  which 


im 


ASTRONOMY. 


' 


>^ 


thuy  luht  tliuy  nffonl  iiiii(jiio  opportuiiitiun  f«*r  iiivuHti^itiii); 
tho  matter  wliivh  Uch  in  tlio  iiiiiiic<]iuto  noighlHirhood  uf 
tho  Mini.  IJiidor  ordiiiury  cinniiiiHtniicofl,  this  inattor  Jh 
rondottid  untiroly  iiiviHihlo  by  the  ufTiil^'iicu  of  tliu  Holnr 
ruyA  which  ilhiiniiiattiouratiiRmpIioro  ;  hutwlieii  a  tMHlyeo 
distant  m  the  moon  '\%  intorpoMMl  Ixjtwoun  tlie  olMiorvor  and 
tlie  Ban,  the  ray^  of  tliu  latter  are  cut  off  from  a  region  a 
hundred  miles  or  more  in  extent.  TIiuh  an  amount  of 
darkness  in  tho  air  is  secured  wliich  \»  lm{)oHHilile  under 
any  other  circumstanceH  wlien  the  sun  is  fur  alN>vo  tho 
horizon.  Still  this  durkness  is  by  no  iiieaiiH  complete,  bccausu 
the  sunlight  is  reflecte<l  from  tlio  region  on  which  the  sun 
is  shining.  An  idea  of  tho  amount  of  darkness  may  lio 
gained  by  considering  that  the  face  of  a  watch  can  be  road 
during  an  eclipse  if  the  oluierver  is  careful  to  shade  his 
eyes  from  the  direct  sunlight  during  tho  few  minutes  be- 
fore the  sun  is  entirely  covered  ;  that  stars  of  the  first 
magnitude  can  be  seen  if  one  knows  where  to  look  for 
them  ;  and  that  all  the  prominent  features  of  tho  land- 
scape remain  plainly  visible.  Au  account  of  the  investi- 
gations made  during  solar  eclipses  belongs  to  the  physical 
constitution  of  tlie  sun,  and  will  therefore  be  given  in  a 
sabseqaent  chapter. 

Oooultation  of  Stan  by  the  Moon. — A  phenomenon 
which,  geometrically  considered,  is  analogous  to  an  eclipse 
of  the  sun  is  the  oooultation  of  a  star  by  the  moon. 
Since  all  the  bodies  of  the  solar  system  are  nearer  than  the 
fflted  stars,  it  is  evident  that  they  must  from  time  to  time 
pass  biBtween  us  and  the  stars.  The  planets  are,  however, 
so  small  that  such  a  passage  is  of  very  rare  occurrence, 
and  -when  it  does  happen  the  star  is  generally  so  faint 
that  it  is  rendered  invisible  by  the  superior  light  of  the 
planet  before  the  latter  touches  it.  There  are  not  more 
than  one  or  two  instances  recorded  in  astronomy  of  a  well- 
authenticated  observation  of  an  actnal  ocoaltation  of  a  star 
by  the  opaque  body  of  a  planet,  although  there  are  several 
cases  in  which  a  planet  has  been  known  to  pass  over  a  star. 


^ituJ. 


■Wfi! 


)»  for  iiivcMti^ititi^ 
J  Tioij<hlM>rho«Hl  uf 
COM,  this  iiiattor  m 
l^uiicu  of  tlio  »M>lar 
l)utwhun  u  iMxlyBo 
n  the  olworvor  aiul 
ff  from  a  region  a 
iiiH  an  amount  of 
impoHHihlu  under 
h  iar  alM>vo  the 
rt  c<»nipleto,  becaunu 
I  on  wliiuh  the  sun 
(larkneiw  may  )hs 
i  watcli  van  be  road 
reful  to  sliado  \m 

0  few  minutes  bo- 
Btars  of  the  first 

where  to  look  for 
turps  of  the  land- 
unt  of  the  investi- 
ngs  to  the  physical 
jfore  be  given  in  a 

I. — A  phenomenon 
logons  to  an  eclipse 
itar  by  the  moon, 
are  nearer  than  the 
i  from  time  to  time 
lanots  are,  however, 
ry  rare  occurrence, 

1  generally  so  faint 
perior  light  of  the 
rhera  are  not  more 
istronomy  of  a  well- 
occnltation  of  a  star 
igh  there  are  several 
1  to  pass  over  a  star. 


(KnmLTArioN  oif  ntahn. 


m 


Rut  the  moon  is  so  largo  and  hur  angular  motion  so  rapid, 
that  she  |>aHHOS  over  Kome  star  visible  to  the  naked  uye 
uvery  few  days.  Such  phononiona  are  toniiod  oi^eultations 
of  star»  hy  the  nwim.  It  mast  not,  however,  be  supposed 
that  they  can  l)e  observed  by  the  naked  eye.  In  general, 
tliu  moon  is  so  bright  that  only  stars  of  the  first  magnitude 
can  Ih)  seen  in  actual  contact  with  her  limb,  and  even  then 
the  ("ontact  must  be  with  the  nnilluminated  limb.  But 
with  the  aid  of  a  telescope,  and  the  pretlictions  given  in 
the  Ephomcris,  two  or  threu  of  thefju  occultations  can  be 
ol)served  during  nearly  every  lunation. 


#' 


I 


1 1^ 


i,'»' 


i    'I'. 


CHAPTER  VIII. 

THE  EAKTH. 

Our  object  in  the  preeent  chapter  is  to  trace  the  ^ecte 

of  terr^trial   gravitation    and    to  study  the  changes  to 

v,rn  is  subject  in  various  places.     Since  every  part 

any  odJ«^  j    ^       ^^  ^ow  belonging  to  the 


« 1- 


„AS8  Airo  MBsrre  ot  tb»  "abth. 


We  begin  by  ««»»  definitioiie  »id  Bome  prmciple.  i«- 
orier  to  make  it  ™»'V™*  *  ,*£fjSoa.  A«M 


II. 


to  trace  the  effects 
idy  the  changes  to 
.     Since  every  part 
irt  as  well  as  every 
that  the  earth  and 
Testrial  form  a  sort 
of  which  are  firmly 
action.     This  attrac- 
mpoBsible  to  project 
Tth  into  the  celestial 
owbelon^ng  to  the 
ain  upon  it  forever. 

p  TBS  BABTH. 
1  some  principles  re- 

etc.  , 

ioA  aBthe  qwmtUy  qf 

this  quantity  of  mat- 
ht  of  the  body— thiB 
orce  of  attraction  be- 
By  the  inertia  of  the 
we  muBt  apply  tott^ 
aite  velocity.  Mathe- 
^two  method*  shwdd 
iment  it  i»  f  ««»<*  ^»"* 


MA88  OP  THE  EARTH. 


189 


the  attraction  of  all  bodies  is  proportional  to  their  inertia. 
In  other  words,  all  bodies,  whatever  their  chemical  consti- 
tntion,  fall  exactly  the  sjune  numl»er  of  feet  in  one  second 
under  tlio  influence  of  gravity,  supposing  them  in  a  vacu- 
um and  at  the  same  place  on  tlie  earth's  surface.  Although 
the  mass  of  a  body  is  most  conveniently  determined  oy  its 
weight,  yet  mass  and  weight  must  not  be  confounded. 

The  vieight  of  a  body  is  the  apparent  force  with  which 
it  is  attracted  toward  the  centre  of  the  earth.  As  we 
shall  see  hereafter,  this  force  is  not  the  same  in  all  parts  of 
the  earth,  nor  at  different  heights  above  the  earth's  sur- 
face. It  is  therefore  a  variable  quantity,  depending  upon 
the  position  of  the  body,  while  the  mass  of  the  body  is  re- 
garded as  something  inherent  in  it,  which  remains  constant 
wherever  the  body  may  be  taken,  even  if  it  is  carried 
through  the  celestial  spaces,  where  its  weight  wonld  be 
reduced  to  almost  nothing. 

The  unit  of  mass  which  we  may  adopt  is  arbitrary  ;  in 
fact,  in  different  cases  different  units  will  be  more  con- 
venient. Generally  the  most  convenient  unit  is  the  weight 
of  a  body  at  some  fixed  place  on  the  earth's  surface — ^the 
city  of  Washington,  for  example.  Suppose  we  take  such 
a  portion  of  the  earth  as  will  weigh  one  Ulogram  in  Wash- 
ington, we  may  then  consider  the  mass  of  that  particular 
lot  of  earth  or  rock  as  a  kilogram,  no  matter  to  what  part 
of  the  universe  we  take  it.  Suppose  also  that  we  conld 
bring  all  tlie  matter  composing  die  earth  to  the  city  of 
'W^ashington,  one  kilogram  at  a  time,  for  the  purpose  of 
weighing  it,  returning  each  kilogram  to  its  place  in  the 
earth  immediately  after  weighing,  so  that  there  should  he 
no  disturbance  of  the  earth  itself.  The  sum  total  of  the 
weights  thus  found  would  be  the  mass  of  the  earth,  and 
would  be  a  perfectly  definite  quantity,  admitting  of  being 
n  kilograms  or  pounds.  We  esn  readily  cal* 
MM  of  a  v<dnme  of  water  equal  to  that  of  the 
ue  we  know  the  magnitiule  of  the  earth  in 
Am  mass  of  one  litee  id  mlm.    Dividii^  &u 


190 


ASTBONOMY. 


into  the  maso  of  the  earth,  Bnppofiing  onrselves  able  to  de- 
termine this  mass,  and  we  shdl  have  the  specific  gravity, 
or  what  is  more  properly  called  the  density  of  the  earth. 

What  we  have  supposed  for  the  earth  we  may  imagine 
for  any  heavenly  body — namely,  that  it  is  brought  to  the 
city  of  Washington  in  small  pieces,  and  there  weighed  one 
piece  at  a  time.  Thns  the  total  mass  of  the  earth  or  any 
heavenly  body  is  a  perfectly  defined  and  determined 
quantity. 

It  may  be  remarked  in  this  connection  that  our  units  of 
weight,  the  pound,  the  kilogram,  etc.,  are  practically  units 
of  mass  rather  tlian  of  weight.  If  we  should  weigh  out 
a  pound  of  tea  in  the  latitude  of  Washington,  and  then 
tidce  it  to  the  equator,  it  would  really  be  less  heavy  at  the 
equator  than  in  Washington  ;  but  if  we  take  a  pound 
weight  with  us,  that  also  would  be  lighter  at  tlie  equator, 
so  that  the  two  would  still  balance  each  other,  and  the  tea 
would  be  still  considered  as  weighing  one  pound.  Since 
things  are  actually  weighed  in  this  way  by  weights  which 
weigh  one  unit  at  some  definite  place,  say  Washington, 
and  which  are  carried  all  over  the  world  without  being 
changed,  it  follows  that  a  body  which  has  any  given 
weight  in  one  place  will,  as  measured  in  this  way,  have 
the  same  apparent  weight  in  any  other  place,  although  its 
real  weight  will  vary.  But  if  a  spring  bidance  or  any 
other  instrument  for  determining  actual  weights  were 
adopted,  then  we  should  find  that  the  wdght  of  the  tame 
body  varied  as  we  took  it  from  one  part  of  the  enrth  to 
another.  Since,  however^  we  do  no^  use  this  sort  of  an 
instrument  in  weighing,  but  pieces  of  metal  which  are 
carried  about  without  <^nge,  it  follows  that  what  we  call 
units  of  weight  are  property  units  of  hums. 

DMurity  of  the  Barth. — ^We  see  that  i^  bodies  aronnd 
us  tend  to  fall  toward  the  centre  of  the  «aiih.  Aeoonfing 
to  the  law  of  gravitation,  this  tendaaey  is  not  8im[4y  a 
single  force  directed  toward  the  oentre  of  tiie  earth,  bnt 
is  the  resultant  of  mi  infinity  of  wsftenSse  f oroes  arising  frmn 


^''SMIiiF' 


MASS  OF  THE  EARTH. 


191 


areelves  able  to  de- 
le  specilic  gravity, 
mty  of  tlio  earth, 
h  we  may  imagine 
t  is  brought  to  tlie 
1  there  weighed  one 
>f  the  earth  or  any 
d    and  determined 

on  that  onr  nnits  of 
are  practically  units 
e  should  weigh  out 
ishington,  and  then 
be  less  heavy  at  the 
iwe  take  a  pound 
hter  at  the  equator, 
ih  other,  and  the  tea 

one  pound.  Since 
R,y  by  weights  which 
JO,  say  Washington, 
irorld  without  being 
hich  has  any  given 
d  in  lihis  way,  have 
r  place,  although  its 
ring  bdance  or  any 
ictusl  weights  were 
>  weight  of  the  same 
I  part  of  the  earth  to 
t  use  this  sort  of  an 

of  metal  which  are 
>W8  that  what  we  call 

lat^l  bodies  around 
ti«  earth.  Aoectt^Bg 
isaey  is  not  simply  a 
tre  of  the  eartii,  but 
lie  f oroes  Mrinng  frrai 


the  attractions  of  all  the  separate  parts  which  compose  the 
earth.  The  question  may  arise,  how  do  we  know  that  each 
particle  of  the  earth  attracts  a  stone  which  falls,  and  that 
the  whole  attraction  does  not  reside  in  the  centre  ?  The 
proofs  of  this  are  numerous,  and  consist  rather  in  the 
exactitude  with  which  the  theory  represents  a  great  mass 
of  disconnected  phenomena  than  in  any  one  principle  ad- 
mitting of  demonstration.  Perhaps,  however,  the  most 
conclusive  proof  is  found  in  the  observed  fact  that  masses 
of  matter  at  the  surface  of  the  earth  do  really  attract  each 
other  as  required  by  the  law  of  Newton.  It  is  found,  for 
example,  that  isolated  mountains  attract  a  plumb-line  in 
their  neighborhood.  The  celebrated  experiment  of  Cav- 
endish was  devised  for  the  purpose  of  measuring  the  at- 
traction of  globes  of  lead.  The  object  of  measuring  this 
attraction,  however,  was  not  to  prove  that  gravitation  re- 
sided in  the  smallest  masses  of  matter,  because  there  was 
no  doubt  of  that,  but  to  determine  the  mean  density  of  the 
earth,  from  which  its  total  mass  may  be  derived  bj  simply 
multiplying  the  density  by  the  volume. 

It  is  noteworthy  that  though  astronomy  affords  us  the 
means  of  determining  with  great  precision  the  rdaUve 
masses  of  the  earth,  the  moon,  and  all  the  pknets,  it  does 
not  enable  us  to  determine  the  absolute  mass  of  any  hea- 
venly body  in  units  of  the  weights  we  use  on  the  earth. 
We  know,  for  instance,  from  astronomioal  rasearch,  that 
the  son  has  about  828,000  times  the  mass  of  the  earth, 
and  the  moon  only  ^  of  tiiis  mass^  bat  to  know  the  abso- 
lute mass  of  either  of  them  we  must  know  how  many 
kili^rams  of  matter  the  eardi  contains.  To  d^ermine 
this,  we  mi^  know  the  mean  douity  of  the  earth,  and  this 
is  something  about  which  direct  observation  can  give  us  no 
inf<Mtnation,  btieanae  we  cannot  penetrate  mora  than  an 
ioaigiiiiaait  distaBoe  nito  the  earth's  interior.  The  only 
way  to  detecmfaie  the  density  of  the  earth  is  to  ifind  how 
mnflb  matter  #  mart  oonteia  in  order  to  attract  bodies  on 
itesnrfaeawttd^alerae  eqnalto  their  observed  weight^ 


lOS 


ASTRONOMY. 


that  is,  Mrith  such  intensity  that  at  the  equator  a  Inxly  sliall 
fall  nearly  ten  metres  in  one  second.  To  find  this  we 
must  know  the  relation  between  the  mass  of  a  body  and 
its  attractive  force.  This  relation  can  be  found  only  by 
measuring  the  attraction  of  a  body  of  known  mass.  An 
attempt  to  do  this  was  made  by  Maskelynr,  Astronomer 
Royal  of  England,  toward  the  close  of  the  last  century, 
the  attracting  object  he  selected  lieing  Mount  Sohehallien 
in  Scotland.  The  speciiic  gravity  of  the  rocks  com])osing 
this  mountain  was  well  enough  knoMm  to  give  at  least  an 
approximate  result.  The  density  of  the  earth  thus  found 
was  4*71.  That  is,  the  earth  has  4.71  times  the  mass  of 
an  equal  volume  of  water.  This  result  is,  however,  un- 
certain, owing  to  the  necessary  uncertainty  respecting  the 
density  of  the  mountain  and  the  rocks  below  it. 

The  Cavendish  experiment  for  determining  the  attrao- 
tion  of  a  pair  of  maasive  balls  affords  a  much  more  perfect 
method  of  determining  this  important  element.  Thd 
most  careful  experittients  by  this  method  were  made  by 
Bailt  of  England  about  the  year  1846.  The  essential 
parts  of  the  apparatus  whidi  he  used  are  as  follows  : 

A  long  narrow  table  T'bearatwo  massive  spheres  of  lead 
W  Wy  one  at  each  end.  This  table  admits  of  being 
turned  around  <m  a  pivot  in  a  borixontal  direction. 
Above  it  is  suspended  a  balance — tliat  is,  a  very  light  deal 
rod  e  with  a  weigh!'  at  each  end  suspended  horisontally 
by  a  fine  silver  wira  or  fibre  of  silk  FE.  The  weights  to 
be  attracted  are  attached  to  each  end  of  the  deal  rod.  The 
right-hand  (me  is  visible,  while  the  other  is  hidden  be- 
hind the  left-hand  weight  W.  In  this  position  it  will  be 
seen  that  the  attraction  of  the  weights  W  tends  to  turn 
the  balance  in  a  direction  opposite  that  of  the  haodl  <rf  a 
watoh.  The  fact  is,  the  bahuiee  begins  to  tarn  in  tUs  di- 
rection, and  being  carried  by  its  own  niomentmn  beyond 
the  point  of  cqnilibrinm,  comes  to  vest  by  a  twist  ^  the 
thread.  It  is  then  carried  part  of  the  way  back  to  its 
original  position,  and  thus  makes  several' ▼ilM«lions>iliiali 


Ifi 


DBNsrrr  of  tbb  barth. 


IM 


I  equator  a  l»ody  sliall 
d.  To  find  this  we 
)  mass  of  a  body  and 
jan  be  found  only  by 
)f  known  masa.  An 
iKKLYNK,  Astronomer 
)  of  the  last  century, 
ig  Mount  Sohehallien 
I  the  rooks  comiMwing 
wn  to  give  at  least  an 

the  earth  thus  found 
:.71  times  the  mass  of 
■esnlt  is,  however,  un- 
rtainty  respecting  the 
ks  below  it. 
etermining  the  attimo* 
\  a  much  more  perfect 
rtant  element.  Thd 
neihod  were  made  by 

1846.     The  essential 
d  are  as  follows  : 
nassi  ve  spheres  of  lead 
able  admits  of  being 

horisontal  diraotioii. 
at  is,  a  very  light  deal 
nupended  horiiontally 
FE.    The  weights  to 

of  the  deal  rod.  The 
e  other  is  hidden  be- 
this  position  it  will  be 
l^ts  W  tends  to  turn 

that  of  the  hao^  of  a 
igins  to  tarn  in  this  di- 
rn  niomentnin  beyond 

test  by  a  twist  of  the 
)f  the  way  bsok  to  its 
)vent'  ilb^oBS  mliioli 


require  several  minutes.  At  length  it  comes  to  rest  in  a 
position  somewhat  different  from  its  original  one.  This 
position  and  the  times  of  vibration  are  all  carefully  noted. 
Then  the  tahle  T  is  turned  nearly  end  for  end,  so  that  one 
weight  TT  shall  be  between  the  observer  and  the  right- 
luuid  ball,  while  the  other  weight  is  beyond  the  left-hand 
ball,  and  the  observation  is  repeated.  A  series  of  observa- 
tions made  iu  this  way  include  attractions  in  alternate  di« 


na.  61  . 

reotions,  giving  a  result  from  which  accidental  errors  will 
be  very  nearly  eliminated. 

A  tibird  method  of  detenniiiiag  the  density  of  the  earth 
is  foiiidMd  on  obserraljons  4Mbe  <^H"^  ^^  ^^  intensity 
of  gmntf  as  we  descend  Wkf*f  the  snrfaoe  into  deep 
mines.  Hie  prinmples  on  wfa^^is  method  rests  will  be 
«q[>lil|lifl  presoitly.  The  most^||^rBfal  tpfdiostion  of  it 
liide  hy  Thnhmm  Aist  in  tj|||  j^srton  Colliery,  Ing- 


194  ABTR0N0M7. 

land.     The  results  of  this  and  the  other  methods  are  as 

follows : 

Oavbitoish  and  Hution,  from  the  attraction  of  balls,  5-32 

R«'C«'  „  a  «         6. 66 

nl'sKkYNB,  from  the  attraction  of  Schehallien 4-71 

AiET,  from  gravity  in  the  Harton  Colliery «-66 

Of  these  different  results,  that  of  Baily  is  probably  the 
best  and  the  most  probable  mean  density  of  the  earth  is 
St  H  times  that%f  water.  This  is  more  than  double 
the  mean  specific  gravity  of  the  materials  which  compose 
the  surfaced  the  earth  ;  it  follows  therefore,  that  the  in- 
ner  portions  of  the  earth  are  much  more  dense  than  its 
outer  portions. 

82.    LAWS  OF  TMRBB8TBIAL  OBAVITATIOir. 

The  earth  being  very  nearly  spherical,  certain  theorems 
respecting  the  attraction  of  spheree^may  be  »ppUed  to  it. 
ThPf undamental  theorems  may  be  regwded  asj^ose 
which  give  the  attraction  of  asphencal  shell  of  matter. 
The  demonstration  of  these^Aeorems  inquires  the  tise  of 
the  Integral  Calculus,  and  will  be  omitted  here,  wily  the 
i^dhioTand  the  results  being  rtated     I^t  usjien  im- 
agine a  hollow  shell  of  matter,  of  which  the  «»ten»^  «^ 
eSemal  surfaces  are  both  spheres,  attnustmg  any  o^« 
masses  of  matter,  a  small  particle  we  may  suppose.     Ttaj 
^e  will  be  attracted  by  every  partide  of  the  A^ 
SSaforce  inversely  as  Ae.qu«e  of  itedj^«m  It 

The  total  attraction  of  the  shd^  wiU  ^e^he  ««d^^ 
this  infinity  of  separate  •*«J~«7«/°'^  .^T^ 
this  reAultimt  by  the  I»t«KnJi^«»*"*\"^^ /TS^Jffl 

cetOrated  in  itt  centre.  ....    .j^rf^^iji  ihsMh 


ATTRAVTION  OF  8PHRRE8. 


195 


lior  methoda  are  aa 

iction  of  balls,  5.32 
i(  <«        5-58 

t(  «        5-66 

hehaUien 4-71 

iiery 6*66 

AiLY  is  probably  the 
isity  of  the  earth  is 
is  more  than  double 
rials  which  compose 
beref  ore,  that  the  in- 
more  dense  than  its 


,  aBAVITATIOli'. 

ioal,  certain  theorems 
may  be  applied  to  it. 
e  regarded  as  those 
ioal  shell  of  matter, 
ui  requires  the  use  of 
mitted  here,  <mly  the 
»d.    Let  UB  thai  im- 
rhich  the  internal  and 
,  attracting  any  other 
e  may  suppose.    This 
r  particle  of  the  shell 
ot  its  distance  from  it 
ill  be  the  nwdtMit  of 
forces.    Detenmning 
lnB,iiiafonnd4liat: 

p  the  JM  wre  cm- 


ponte  attraeiiong  in  every  direction  vnU  neutralize  each 
(tther,  no  matter  whereahout*  in  the  interior  t/ie  particle 
may  be,  and  t/ie  resultant  attraction  qft/ie  s/iell  will  there- 
fore be  zero. 

To  apply  tliis  to  the  attraction  of  a  solid  sphere,  let  us 
first  suppose  a  body  either  outside  the  sphere  or  on  its  sur- 
face. If  we  conceive  the  sphere  as  made  up  of  a  great 
number  of  spherical  shells,  the  attracted  point  will  be  ex- 
ternal to  all  of  them.  Since  each  shell  attracts  aa  if  its 
whole  mass  were  in  the  centre,  it 
follows  that  the  whole  sphere  at- 
tracts a  body  upon  the  outside  of 
its  surface  as  if  its  entire  mass 
were  concentrated  at  its  centre. 

Let  us  now  suppose  the  attract- 
ed particle  inside  the  sphere,  as 
at  Py  Fig.  66,  and  imagine  a 
spherical  surface  P  Q  conoeutric 
with  the  sphere  and  passing 
through  the  attracted  particle. 
All  that  portion  of  the  sphere  lying  outside  this  spherical 
surface  will  be  a  spherical  shell  having  the  particle  inside 
of  it,  and  will  therefore  exert  no  attraction  whatever  on 
the  particle.  That  portion  inside  the  surface  will  con- 
stitute a  sphere  with  the  partide  oi|  its  surface,  and  will 
therefore  attract  as  if  all  this  portion  were  concentrated 
in  the  centre.  To  find  what  this  attraction  will  be,  let  us 
first  snppoee  the  whole  sphere  of  equal  dennty.  Let  us 
pat  •> 

Oj  the  radius  of  the  entire  sphere, 
r,  the  diptanoe  P  Cot  the  particle  from  the  centre. 
The  total  volume  of  matter  inside  the  sphere  jP  Q  will 

then  be,  by  geemetiy,  j  jr  r*.    Dividing  by  ihe  square  of 


Vto.  M. 


the  (^stattoe  r;  we 
sented  hj 


that  ti)e  attraetion  will  be  re^e- 


iiiili<sutwi>iuaWMWBa 


*ttm 


J96  AamoNOMr. 

that  is,  inside  the  sphere  the  attruction  will  be  f  Jf^'^y  " 


•6 


■>ra. 


Onteide  the  surface  the  whole  volume  of  the  sphere  3  »r  «' 
will  attract  the  particle,  and  the  attraction  will  be 

—    TT    — ;• 

3       r" 

If  we  put  r  =  a  in  this  formula,  we  shall  have  the  same 
r«mlt  is  before  for  the  surface  attraction. 

uJ  iL  nexr.«pp««  that  the  density  of  the  sphere  va- 
riilmrllJnrits  surface,  b«t  in  Buch  aw^y  as  o 
wTnanal  at  equia  distances  fnim  the  centre.  We  may 
SL^^^iv^Jit  as  formed  of  an  infinity  of  concentric 
^eSldU«Lh  homogeneous  in  density,  but  not  of 

2>,  the  mean  density  of  the  .hell  outside  the  pa^^^^^ 
/)',  the  mean  density  of  the  porUon  F  Q  mside  of  /-. 
We  shall  then  have: 

Volume  of  the  Bhell,,^^ « («*  -  O- 

Volume  of  the  inner  sphere,  ^  « t'. 

Massof  theshell  =  vol.x/)  =  |'ri>(a'-0- 

Mass  of  the  inner  sphere  =  vol.  x  2>'  =  g  'f  -^  ♦'• 
M^ofwholesphere^tomofm^-eaofAeUandinner 

«phe«=|'r(2)a'-|-(i>'-i>)4 


ATTH ACTION  OF  SPUKRKa. 


197 


•n  will  be  directly  a» 

centre.     If  the  par- 

aiid  the  attraction  ia 


e  of  the  sphere  g»r  a 
action  will  be 


>  Bhall  have  the  aame 
iCtion. 

Bity  of  the  sphere  va- 
Bt  in  Buoh  a  way  as  to 
the  centre.    We  may 
1  infinity  of  concentric 
in  density,  but  not  of 
Theorems  I.  and  II. 
It  will  not  be  the  same 
>here  for  a  particle  in- 
.  66,  let  US  put 
outside  the  particle  P. 
■tion  P  Q  in«de  of  P. 

1.x  2>'  =  |'r />'»'. 
manes  of  ahell  and  inner 


Attraction  of  the  whole  sphere  upon  a  point  at  its  snr- 

Attraction  of  the  inner  sphere  (the  same  as  that  of  the 

_      Mass       4      -y 
whole  shell)  upon  a  pomt  at  /'  =  -p—  =  g  ^  x/^  »*• 

If,  as  in  the  case  of  the  earth,  the  density  continually  in- 
creases toward  the  centre,  the  value  of  />'  will  increase 
also  as  r  diminishes,  so  that  gravity  will  diminish  less 
rapidly  than  in  the  case  of  a  homogeneous  sphere,  and 
may,  in  fact,  actually  increase.  To  show  this,  let  us  sub- 
tract the  attraction  at  P  fiom  that  at  the  surface.  The 
difference  will  give : 

Diminution  At  P  =  ^ir  {Da+{iy  -  D)-^  -  D' r). 

Now,  let  us  suppose  r  a  very  little  less  than  a,  and  put 
r=:a  —d, 

d  will  then  be  the  depth  of  the  particle  below  the  surface. 
Cubing  this  value  of  r,  n^leoting  the  higher  powers  of 
d,  and  dividing  by  a*,  we  find, 


Substituting  in  the  above  equation,  the  diminution  of  grav- 
ity  at  P  becomes, 

..,      (SD'-ilTid. 

We  see  that  if  8i>  <  32>',  that  is,  if  the  density  at  tiie 
surface  is  leas  than  f  of  the  mean  density  of  the  whole  in- 
ner mass,  this  qvantity  will  beoome  negative,  showing  that 
the  f oroe  of  gravity  will  be  less  at  the  surf  atia  than  at  a 
small  depth  in  the  interior.  But  it  must  ultimately 
diminish^  because  it  is  necessarily  aero  at  the  centre, 
tt  was  on  this  principle  that  Professor  Airy  determined 
the  density  of  the  earth  by  oomparing  the  vibrations 


108 


ASTRONOMY. 


of  a  pendnlnm  at  the  bottom  of  the  Harton  ColUery,  and 
at  the  Burface  of  the  ear  h  in  the  neighborhood.  At  the 
bottom  of  the  mine  the  pendnlnm  gained  about  2*. 6  per 
day,  showing  the  force  of  gravity  to  be  greater  than  at  the 
Burfaoe. 

8  8.  nouBi  Airo  MAOirrruOT  of  th«  sabth. 

If  the  earth  were  fluid  and  did  not  rotate  on  its  axia,  it 
would  aBBume  the  form  of  a  perfect  sphere.    The  opinion 
is  entertained  that  the  earth  was  once  in  a  molten  state, 
and  that  this  is  the  origin  of  its  present  nearly  spherical 
form.     If  we  give  such  a  sphere  a  rotation  upon  its  axis, 
the  centrifugal  force  at  the  equator  acts  in  a  direction  op- 
posed  to  gravity,  and  thus  tends  to  enkrge  the  circle  of 
STequator.    It  is  found  by  mathematical  analysw  that 
the  form  of  auch  a  revolving  fluid  sphere,  supposing  it  to 
be  perfectly  homogeneous,  will  be  an  oblate  ellipsoid— that 
is,  all  the  meridians  will  be  equal  and  similar  elbpses,  hav- 
ing  their  major  axes  in  the  equator  of  the  sphere  and  their 
ndnor  axes  coincident  with  the  axis  of  rotation.    Our  wi^, 
however,  is  not  wholly  fluid,  aad  Ihe  wMty  ol  ita  oonti- 
nents prevents ite  asraming the  Um  it ▼onWtake if  tibe 
ocean  covered  its  entire  surface.  When  we  speA  of  tiui  fig- 
ure of  the  earth,  we  mean,  not  theoi^e  of  the  ^  Hid 
liquid  portions  respectively,  but  the  figure  whieh  it  wwW 
assume  if  its  entire  surface  were  an  ocean.    Let  wim^ffP 
eanakdug  down  to  the  ocean  level  in  every  aire«ioa 
through  the  eontineota,  and  the  water  of  JheoeaM  to^be 
adnrfSed  into  them.    Then  the  onrted  surlloe  toutihtog 
the  water  in  all  these  oanab,  and  ooliloideiit  wi&^the  ■»- 
face  of  the  ocean,  is  that  of  the  ideal  earth  conaldewd*^ 
Mrtronomers.    By  the  figure  of  the  e«*h  »  meant  ^ 
figure  of  this  liquid  surface,without  refereneetothem- 
equalitiesof  thesoUdsurfaoe.  „,     « 
We  cannot  say  that  this  ideal  earth  is  a  perfeet  eiUpM»ia, 
beoanaewe  know  that  the  interior  ia  not  homogiBeoBi, 


■.  .t'tMimm^'ftimmm 


MRAHUBMMENT  OF  THE  BAHTH. 


199 


larton  Colliery,  and 
ghborhood.  At  the 
lined  about  2* -5  per 
B  greater  than  at  the 


OF  THS  SABTH. 

i  rotate  on  its  axis,  it 
phere.    The  opinion 
30  in  a  molten  state, 
sent  nearly  spherical 
utation  upon  its  axil, 
tcts  in  a  direction  op« 
enlarge  the  circle  of 
mati(»l  analysis  that 
phere,  supposing  it  to 
oblate  ellipeoid— that 
I  similar  ellipses,  hav- 
f  the  sphere  and  their 
rotation.    Our  earth, 
e  solidity  of  its  eonti- 
a  it  would  take  if  the 
en  we  speak  of  the  %- 
Ddhte  of  the  solid  and 
fipire  whidiii  would 
eean.    Lei  v»imi#Bbe 
el  in  evety  diradtkm 
\iBttA  theooeaa  to  he 
nred  svrfioe  ton^iiig 
^ddent  with  the  snr- 
»!  earth  eoiindered  by 
e  flttdi  is  mesnt  ih» 
at  ref««nee  to  tlie  in- 

b  is  a  perfect  elUpM»ld, 
:  is  not  homcfeaMMM, 


but  all  the  geodetic  measures  heretofore  made  are  so  nearly 
represented  by  the  hypothesis  of  an  ellipsoid  that  the  lat- 
ter is  considered  as  a  very  close  approximation  to  the  true 
liguro.  The  deviations  hitherto  noticed  are  of  so  irregu- 
lar a  character  that  they  have  not  yet  been  reduced  to  any 
certain  law.  The  largest  which  have  been  observed  seem 
to  be  due  to  the  attraction  of  mountains,  or  to  inequalities 
of  density  beneath  the  surface. 

Method  of  Ttiangulation. — Since  it  is  practically  im- 
possible to  measure  around  or  through  the  earth,  the  mag- 
nitude as  well  as  the  form  of  our  pknet  has  to  be  found 
by  combining  measurements  on  its  surface  with  astronom- 
ical observations.  Even  a  measurement  on  the  earth's 
Hurface  made  in  the  usual  way  of  surveyors  would  be  im- 
practicable, owing  to  the  intervention  of  mountains,  rivers, 
forests,  and  other  natural  obstacles.  The  method  of  tri- 
angubtion  is  therefore  miiversally  adopted  for  measure- 
meuls  extending  over  hu^  areas.  A  triangnlation  is  ex- 
ecuted in  the  folbwing  way :  Two  points,  a  and  (,  a  few 


nuiea  q^wt,  an  ntooled  m  the  e«traniti«  of  •  bwe-UiM. 
They  most  be  so  ehosm  that  thebr  distanee  apwt  ean  be 
aoMMliity  meimred  by  rodi;  ^  intorvoaing  ground 
shooiiiittoMfora  be  as  level  and  fk«e  f nAn  obstruction  as 
poiJJili  Om  or  mora  etevated  points,  J'j;  ete.,  must 
be  ^bttld  Itoot  one  or  hiifc  ends  of  iSa^  bese-Iiiw.    ^~ 


mmrnttm 


800 


ASTROyOMT. 


means  of  a  theodolite  and  by  obwrvatlon  of  tl»o  polo-Btar, 
the  dlrectionB  of  these  points  relative  to  the  meridian  are 
accurately  observed  from  fih  end  of  the  base,  as  ii»  also 
the  direction  a  A  of  the  baie-lino  itself.  Suppose  i^^  to 
be  a  point  visible  from  each  end  of  the  Imse,  then  in  the 
triangle  abFvio  have  the  length  a  h  determined  by  actual 
measurement,  and  the  angles  at  a  and  J  determined  by  ob-^ 
servations.  With  those  data  the  lengths  of  the  sides  aF 
and  hFKm  determined  by  a  simple  trigonometrical  com- 
putation. 

The  observer  then  transports  his  instruments  to  F^  and 
determines  in  succession  the  direction  of  the  elevated 
points  or  hills  DEO HJ,  etc.  He  next  goes  in  succes- 
sion to  each  of  these  hilhi,  and  determines  the  direction  of 
all  the  others  which  are  visible  from  it.  Thus  a  network 
of  triangles  is  formed,  of  which  all  the  angles  are  observed 
with  the  theodolite,  while  the  sides  are  successively  calcu- 
hited  trigonometrically  from  the  first  base.  For  instance, 
we  have  just  shown  how  the  side  a  J*  k  calculated  ;  this 
fonns  a  b«n  for  the  triangle  EF^,  the  two  remaining 
aides  of  whioh  wt  ooouMtoO.  Hm  aid*  Xf  fonns  the 
biw  of  the  triaai^  OBF,  fho  dite  of  wMoh  aro  cakm- 
liifeed,  efee.  In  tiife  qpente  now  aa^  aie  obMired 
thm  ai«  theoratieaOy  aeeMMiy  to  edenlrto  tlw  trianglea. 
Tbb  amplw  of  ai«»  Mrrca  to  teroia  <Im  doiMlion  of  any 

«K|on  in  «lie  MMHwa,  iokl  to  t«rt  OmDt  amtMej  \ij  the 
9mvuaetAiAt^tmiS»M.    AoeuMlalfaig  «mc«  tie  fvr- 

time  to  tiDM  ••  oppertttBitj  oAnk 

Ohaino  oi  triangles  have  thus  been  meanired  in  Buaiia 
from  the  Danube  to  the  Arctic  Ocean,  in  England  and 
Fimnoe  from  the  Hebrides  to  Algien,  in  this  oountiy  down 
nearly  onr  entuw  Athmtio  coaat  and  along  the  great  lakes, 
and  through  short  distanoea  in  numy  other  boontriea. 
An  east  and  west  Ihie  is  now  being  run  by  the  Coast  Sur- 
vey from  the  Atlantic  to  the  Pacifie  Ocean.  Indeed  it 
may  be  expected  that  a  network  of  triaaglM  will  bo  gmd- 


MAONITUDB  OF  THK  KARTU. 


301 


»n  of  tliu  polu-star, 
o  the  meridian  aro 
tho  base,  as  iii  aim) 
If.  Buppoms  F  to 
u  iNune,  then  in  the 
)tennined  by  actual 
h  detennined  by  oh- 
lis  of  the  sides  a  F 
rigonometrieal  coiii- 

trnments  to  F.,  and 
)Q   of  the   elevated 
text  goes  in  succes- 
ines  the  direction  of 
Thus  a  network 
angles  are  observed 
e  successively  oalcu- 
iMse.     For  instance, 
'  la  calculated  ;  this 
the  two  remaining 
id*  XJF  fonu  the 
of  wUdh  wo  oalen- 
ia|^  are  dwerved 
0iilito  tha  triangles. 
Om  deieetkMi  of  anjr 
kflk  MeunejVthe 
liHag  CROI*  ue  fmr- 
AdikimMAiUeiiram 

meMured  inBuadla 
Mtt,  in  England  and 
in  thia  oonntry  down 
long  the  great  lake*, 
iny  other  bonnkiiea. 
in  by  the  Ooert  Snr- 
B  Ooean.  Indeed  it 
rianglea  will  be  gnd. 


MUOH 


ually  extenchid  «>vor  tho  snrface  of  every  civillxod  country, 
ifi  ordur  to  conBtfliot  perfect  maps  of  it. 

Siippoflo  that  we  taka  two  stations  situatod  north 
and  south  of  each  other,  deterinino  tho  latitude  of  each, 
and  measure  the  distance  between  them.  It  is  evident  that 
l>y  dividing  the  distance  in  kilometres  by  tho  difference  of 
latitude  in  degrees,  we  shall  have  the  length  of  one  degree 
of  latitude.  Then  if  tho  earth  were  a  sphere,  we  should 
at  once  have  its  circumference  by  multiplying  the  length 
of  one  degree  by  860.  It  is  thus  found,  in  a  rough  way, 
that  the  lengtli  of  a  degree  is  a  little  more  than  111  kilo- 
metres, or  between  69  and  7U  English  statute  miles.  Its 
circumference  is  therefore  about  40,()00  kilometres,  and 
its  diameter  between  12,000  and  13,000.* 

Owing  to  the  elliptioity  of  the  earth,  the  length  of  one 
degree  varies  with  the  latitude  and  the  direction  in  whioh 
it  is  measured.  Tlie  next  step  in  the  order  of  accuracy  i> 
to  find  tha  nia|;nitnde  and  the  form  of  the  earth  from 
measures  of  hng  aroi  iA  laiitnde  (and  aometimea  of  longi- 
tude) made  ini  Afferent  regions,  eqiedally  near  the  equa- 
tor and  in  M^  latitodes.  Bnt  we  shall  still  find  that  dif - 
ferent  oombinaiions  of  measnrss  i^re  slightly  different  re- 
sults, hd0k  for  the  ni4piitnde  and  the  eUiptidty,  owing 
to  the  iiMilaritias  in  the  Section  of  attraction  whioh  we 
have  alftaly  disoribed.  ^m  pcoblem  is  therefore  to  find 
what  el%iioid  will  wMtj  ^  inaaMms  with  fha  least  sum 
total  of  mw.  Kaw  and  more  aatmrata  sohtlons  will  be 
reached  fiom  time  to  time  as  geodatie  measorss  are  extend- 
ed over  a  wider  area.  The  following  are  among  the  most 
recent  results  hitherto  reached:  Listuto  of  Gdttiagen 
in  187S  found  tbo  earth's  pokr  semidiameter,6866  •270  kilo- 

*  Wim  the  metric  qrstm  was  origiiuaiy  designed  by  the  Franoh.  It 
waswiMedtiMtthe  kUooMtra  rtMuU  be  Tii«9  of  the  dbtanoe  from 
the  pgis  of  dearth  to  the  equator.  This  would  make  a  dogree  of  the 
iMNn«»,t»inikiloaMtNo.  Bat.owfaiftotte 
loC  WMMBiiaff  a  awridka  of  the  earth,  the  oetf»> 
I  with  tbs  BMtn  aetodljr  adopted  is  not  exact. 


wm 


202  ABTBONOMF. 

metres;  eartli's  equatorial  Bemidiameter,  6377-877  kilo- 
metres  ;  earth's  compression,  j^  of  the  equatorial  di- 
ameter;  earth's  eccentricity  of  meridian,  0.08319.  An- 
other  r4nlt  is  that  of  Captain  Clarke  of  England,  who 
found :  Polar  semidiameter,  6356-456  *  kilometres ;  equa- 
torial semidiameter,  6378.191  kUometres. 

It  was  once  supposed  that  the  measures  were  shghtly  bet- 
ter represented  by  supposing  the  earth  to  be  an  elhpsoid 
with  three  unequal  axes,  the  equator  itself  being  an  elhpse 
of  which  the  longest  diameter  was  600  metres,  or  about 
one  third  of  a  mile,  longer  than  the  shortest.  Thisrescdt 
was  probably  due  to  irregularities  of  gravity  m  those  parts 
of  the  continents  over  which  the  geodetic  measures  have 
extended  and  is  now  abandoned. 

ae<,gt»phio  and  Geooentrio  L»tltudei. -An  obviouB  re- 
sult of  the  eUipticity  of  the  earth  is  that  the  plumb-lme 


does  not  point  toward  the  earth's  oentee.  Jf^'f^ 
represent  a  meridional  section  of  the  earfh,  ^^^^2 
axis  of  rotation,  JEQ  the  plane  of  ^J^^*  «f^  ^ 
position  of  the  observer.    The  Une  MS,  trogent  tcr  tte 

beentdBenasft.tflOOTi. 


■  i)imuu'LiijiiiLi.iiii.uiiwti»mwjjliiiimw'wiu 


mMN 


MhMck 


FOmB  OF  OBAVITT. 


ter,  6377-377  kilo- 
)f  the  equatorial  di- 
ian,  0.08319.  An- 
LE  of  England,  who 
*  kilometres ;  equa- 
res. 

roB  were  slightly  bet- 
ii  to  be  an  ellipsoid 
tself  being  an  ellipse 
>00  metres,  or  aboat 
liortest.  This  result 
jravity  in  those  parts 
detic  measares  have 

idM. — An  obvions  re- 
that  the  plumb-line 


earth  at  0^  will  then  represent  the  horizon  of  the  observer, 
while  the  line  Z  jV',  perpendicular  to  B  B,  and  therefore 
normal  to  the  earth  at  Q,  will  be  vertical  as  determined 
by  the  plumb-line.  The  angle  O  JV'Qy  or  ZO  Q\  which 
the  observer's  zenith  makes  with  the  equator,  will  then  be 
his  astronomical  or  geographical  latitude.  This  is  the  lat- 
itude which  in  practice  we  nearly  always  have  to  use,  be- 
cause we  are  obliged  to  determine  latitude  by  astronomical 
observation,  and  not  by  measurement  from  the  equator. 
We  cannot  determine  the  direction  of  the  true  centre  0  of 
the  earth  by  direct  observation  of  any  kind,  but  only  that 
of  the  plumb-line,  or  of  the  perpendicular  to  a  fluid  sur- 
face. ZOQ'  ia  tiierefore  the  astronomical  latitude.  If, 
however,  we  conceive  the  line  GOz  drawn  from  the  cen- 
tre of  the  earth  through  0,  z  will  be  the  observer's  geo- 
cmtrio  tmkhj  while  the  angle  O  CQ  will  be  his  geoom- 
trie  latitude.  It  will  be  observed  that  it  is  the  geocentric 
and  not  the  geographic  latitude  which  gives  the  true  posi- 
tion of  the  observer  reUtive  to  the  earth's  centre.  The 
difference  between  the  two  latitudes  is  the  atigle  CO  If' 
or  ZO0;  this  is  called  the  an^<2<^M««0r^»oa{.  Itiszero 
at  the  poles  and  at  the  eqnatw,  because  here  the  normals 
pass  tlm>ngh  the  omtre  of  the  dlipse,  and  it  attains  its 
maximum  of  11'  80'  at  ktitode  46**.  It  will  be  seen  that 
the  geocentric  Ittdtnde  is  always  less  than  the  geographio. 
In  north  latitudes  the  geooentrio  Mi^th  is  south  <xf  the  ap- 
parent ioiitii  and  in  southon  kulltndes  n<«tlk  oi  it,  being 
nearer  the  equator  in  each  case. 


centre.    Let  Fig.  6$ 

.earth,  JV^iS  bong  the 

le  equittHT,  and  O  the 

MSy  tMigent  tir  the 

Mk,  tiM  polar  mdlHB  M« 


g  4.  casujxQM  or  OBAViro  wins  tbm  "lkti- 

If  flwanfbwena  p«rf«ctq^wra,  and  didnol  rotate  OB  its  azta,tl»e 
iateatl^  of  gnvil^  would  be  tile  iaiiieovw  its  oitinmvfso^  llwra 
baiNibivarialJkMiftom  two  OMues,  Moiely,  (1}  The  dtt]^  fom 
of  enr  dlflbe,  and  (n  the  entrifiMal  ftoras  flmuMted  bv  its  rotatina 
OB  Hh  «ds.  eUgkOj  fuMng.  Ow  latterli  aot  a  ebHige  in  tike 
real  fpiM  of  gtvmj.  «  of  u»  earth's  sMnetiiHi,  but  onl^  aa 
appaMHt  forae  <rf  aaMMr  IdaA  aettait  in  oppedkloii  to  gmvity. 


— iiiiiiijMHimjiii,  luiiimiiiiiaMi 


304 


ASTRONOMY. 


The  intensity  of  gravity  i«  mewured  by  the  dirtance  "Wch  » 
heavy  bodyin  a  vacuum  Will  fall  in  a  unit  of  time,  «ay  one  second. 
eS  10  metres  or  82  feet  may  be  regarded  as  a  ^ugh  approj™.- 
Son  to  its  value.  There  are,  however,  so  many  practical  difflcol- 
iS  in  the  way  of  measuring  with  precision  the  distwice  a  body 
fS,  ta  one  second,  that  theWe  of  gravitv  is,  in  Vf»^^\^^- 
Xed  indirectly  by  finding  the  lengtl  of  tlie  »f?»^J^.  I?"3^ 
uL  shown  in  mechanica  that  if  a  pendulum  of  length  ^  vttarrtes 
in  a  tSrV  a  heavy  body  will  in  this  time  T  fall  through  the 
^TL,n  beingSe  ratfo  of  the  circumference  of  a  drcle  to  it. 
Keter.  '(.r=8.f4169  .  .  .  ,r'=».86eM4.)  Therefore,  to  find  fte 
force  of  gravity  we  have  only  to  determtoe  the  length  of  the 
gecond's  Mndulum,  and  multiply  it  by  this  factor. 

The  drtermination  of  the  mean  attractive  force  of  the  wrfh  is 
Important  in  order  that  we  may  compute  its  -ctlon  on  Oiemoon 
Srother  heavenly  bodie.,whife  the  variation  oj  »"»  «""«J»° 
afford  us  data  for  judging  of  the  variations  of  denrity  in  the  wth  s 
Sterio?^  Sentifio  Seditions  have  therefore  taken  pains  to 
d^Vndne  thelength  of  *Se  «)cond's  pendulum  «*»«»»•««»  P^*» 

Snirglobe.  ^  do  tWs,  it  is  °»t  "r^.lV'^L  nS^SJJ 
actually  measure  the  length  of  the  pendulum  at  all  *!»«  P*^  »«? 
visit.  They  have  only  to  carry  some  one pendulmnof  •  ▼e^  ■»«» 
oonstruction  to  each  want  of  observation,  and  observe  how  many 

SSSTS  mri.es  inTday.  7^^ '^""HJ^/lSSi' ?!& 
ia  proportional  to  the  aooare  of  the  nmnber  of  '^^'^^^^'°^ 
maiSter  the  voyage,  they  count  the  vibrations  •* jwine  "tonoard 
Sinf-li»Sn  fSSitoiiw.  Thua,  by  simply  «uariiigthe»nm^r 
5f  vibratiomi  and  comparing  the  squares,  ti»ey  hj^f  ^«<J» 
vridch  gravity  at  varioaTpSnta  of  «he  earth's  surface  bewrs  to 
JSSy™l2ndon.  »  ia'tiien  only  necessary  to  ^t««in^ 
SSeolute  intenrfty  of  gravity  at  London  toinfer  It  at  aU  the 
StSr  points  for  which  the  rrtio  is  known.  From  •  «««»  ™»S 
S  SJSrvatiomi  of  tills  kind,  it  is  fimnd  timt  tiie  feigth  of  ^ 
second's  pendulum  in  Uititude  ^  may  be  nearly  repiweiited  by  tiie 
equation,  ,  ,  ^ 

£  =  ()••  W<>W(1  +  0-006»9  mnV). 

Prom  this,  the   force  of   gravity  is  found  by  mnltipiyiiig  bj 
ir*  =  9-86M,  giving  the  result : 

y'  =  9--7807(l +0-0M808ln**). 

Tliese  formuhe  show  that  the  awperent  force  of  gravity  iooeaeM 
bv  a  Sle  SiTthan  ^  of  its  wteto  aiiMmnt  from  the  jWMjorto 
ge  X  m  cTrSllly  caicuWe  bow  »««»  •? ^?^«^ 
at  the  eouator  is  due  to  the  oeutrifiigal  f«ce  of  the  eeim  a  (OwMa. 
By^^rtSL  of  mechanic  tiie  Mutrifugri  force  is  given  by  the 
eqmtion, 


.wuiiftiiimni 


TBBRS8TRIAL  GRAVITY. 


205 


the  distance  which  % 
time,  aay  one  second. 
IS  a  rough  approxima- 
any  practical  difHcul- 

the  distance  a  body 

is,  in  practice,  deter- 
le  second's  pendulum, 
n  of  lensth  L  vilnrates 
ae  T  fall  through  the 
irenoe  of  a  circle  to  its 

Therefore,  to  find  the 
ae  the  length  of  the 
actor. 

e  force  of  the  earth  is 
to  action  on  the  moon 
ions  of  tUs  attraction 
>f  denidty  in  the  earth's 
lefore  taken  pains  to 
Imn  at  numerous  pointa 
isary  that  they  snould 
a  at  all  the  places  they 
mdnlmn  of  a  very  solid 
and  obsenre  how  many 
tiat  the  force  of  gnvity 

of  TihratioBi.  Before 
tions  at  some  standard 
dy  squaring  the  number 
i,  they  have  the  ratio 
■rth's  snrfaee  bears  to 
Mary  to  determine  the 

to  infer  it  at  aU  the 

From  a  gnat  number 

that  the  feigth  of  the 

larly  repraaeated  by  the 

iBinV). 

md  by  mnltiplyiBg  bf 

lain**). 

'orce  of  gravity  inenaiea 
«nt  frov  tiie  equator  to 
moett  of  the  dio^iatioa 
ie  of  the  ewrth'a  fOtaAk^ 
igalfcHroeisJI^raibythe 


T  beinir  the  time  of  one  revolution,  and  r  the  radius  of  the  cirole  of 
STtton.  Supposing  the  earth  a  Bphe«,  J'Wch  will  cause  no 
KoSnt  errifin  our  present  calculation  the  distance  »'  »  P^J"* 
SiKiith's  surface  ii  latitude  ^  from  the  axis  of  rotation  of  the 


A  being  the  earth's  radius, 
therefore 


The  centrifugal  force  in  latitude  f  is 


4«*acoBf 

But  this  force  does  not  act  in  the  direction  non>»»  ^*^,«^|''? 
surfiS:  but  perpendiciUar  to  the  axis  of  tiie  earth,  which  direction 
mlk^he  anSe  ♦  with  the  normal.    We  may  therefore  resolve  the 

SSb  iitS  Xd-Tponento,  "f./'^V''^""*  *««^'»iSi're 
toWard  tiie  equator,^e  other./  coa  ♦,  downward  toward  He  centre. 
STe "rat  component  makes  the  earth  a  P~««te  e»«P^  "iKS 
shown,  while  the  second  acta  in  «PP«««Jo°  *»,F»'S;.«t 
^Sug^  force,  therefore,  dfaniniahes  gravity  by  tKe  amount, 


/cosf  = 


iir'acoa*^ 


T* 


T  the  sidereal  day,  is  86,164  seconds  of  mean  time,  while  o,  for 
Se  eJJSTi.  M77.877  metres.  Substituting  in  this  expresdon, 
the  oentrifngri  forc«»  becomes- 

/co»f  =  0-088»lcoa«  f  =0-.08«»l  (1 -sin*^), 

or  .t  the  equator  a  little  more  than  Hw  A*  'o**"  °  uf  «ffi;  J2,* 
S^niionlorthe  apparent  foree  o*„««~:»*y  SI  fa^ 
which  we  have  alreiSfyfound,  may  be  put  in  flie  form, 

/  =»-.T807  +  0».0BO87ain»f. 

This  is  the  true  force  of  gravity  diminished  by  the  «»«trifu«l 
SS>rthereftore,  to  find  that  true  fbree  we  muatadd  the  centri. 
f  1^  foree  to  it,  giving  the  reault : 

a  =  9*-8146  +  0--01696ehiV 
=  9-.8146  (1 -I- 00017<8sbi*f), 

for  tiie  i«al  attraction  of  tiie  sphiiroidal  earth  upon  a  body  on  ita 
aorfiaBe  in  latitude  f . 


It  Witt  be  iBta^*l«to  oompwe  thfa  »^tt.r?L*%?^?^ 
a  hftvtog  the  I 


ofa«Bb«Nidhft^-- 
by  labgn^fiott  tiial  if  «, 


letU 


idty  aa  the  ea»:h.    It  is  fbond 

small,  be  the  eoeeatridity  v/l  a 

aad  9*  ita  attfaction,apoB  a  body 


SLutSSMMiahiatit  •mpB^  "rf  »•  «•  attfactioii,«poB  a  body 
STSS^rfSf^'SSK'.^  fwiU  be  given  by  the 


,:;,„0  +  f-dnV). 


10 


906 


ABTRONOMT. 


V^0*  =  OOOO667;  m  that 


In  the  caie  of  the  earth,  «  =  00817 
the  eipresrion  for  gravity  would  be, 

9  =  9.  (1  +  0000667  sin*^). 

We  see  that  the  factor  of  aln*  ♦,  which  expresses  the  ratio  in 
which  cravity  at  the  poles  exceeds  that  at  the  eouator,  has  less  than 
half  the  value  (001780),  which  we  have  found  from  observation. 
This  difference  arises  from  the  fact  that  the  earth  is  n^  hooiogenu- 
ous,  but  increases  in  density  from  the  surface  toward  the  centre. 
To  see  how  this  result  follows,  let  us  first  inquire  how  the  earth 
would  attract  bodies  where  its  surface  now  is  if  its  whole  mass 
were  concentrated  in  its  centre.  The  distance  of  the  equator 
from  the  centre  is  to  that  of  the  poles  from  the  centre  as  1  to 
VT^^.  Therefore,  in  the  case  supposed,  attraction  at  the  equator 
would  be  to  attiM^on  at  the  poles  t»\—f  to  1.  The  ratio  of  in- 
crease of  attraction  at  the  poles  is  therefore  in  this  extreme  case 
about  ten  tfanes  what  it  is  for  the  hoDKwenoous  elUpsoid.  We  oon^ 
dude,  therefore,  that  the  more  newly  Oie  earth  approaches  ttjfa 
extreme  case— that  is,  the  more  it  increases  u  denrity  toward  the 
centre— the  greater  will  be  the  dffierenoe  of  attraction  at  the  poles 
and  the  equator. 


l\ 


8  6.  isxynas  or  thh  sabtipb  axis,  ob  pre- 

GBBSIOir  OF  THX  aQXTINOXBS. 

Sidanal  and  Bquinoctiia  TeMr.— In  describing  the  ap- 
parent  motion  of  the  sun,  two  ways  were  shown  of  find- 
uig  the  time  of  its  apparent  revolntion  around  the  sphere 
—in  other  words,  of  fixing  the  length  of  a  year.    One  of 
these  methods  oonnsts  in  finding  the  interval  betweeM  snc- 
oestiTe  passages  through  the  equinoxes,  or,  which  is  the 
game  thing,  across  the  plane  of  the  equator,  and  the  other 
by  finding  when  it  returns  to  the  same  positiw  among 
the  Stan.    Two  thousand  years  ngft,  Hippabohos  found, 
by  comparing  his  own  obaervationa  with  those  made  two 
centuries  before  by  Timoohabis,  ttit  these  two  methods 
of  fixing  the  length  of  the  year  ^  not  gbe  the  iame 
rendt    It  had  preTioody  beeo  ^iso^dflrad  ilw*  the  teqgth 
of  a  year  was  about  86^^^  "ad  inattemptiilgtoooR«nt 
this  period  by  oomplinng  hk  obnrvsd  tinifla  of  the  snii*i 
poBBhig  tiw  equinox  with  those  of  Tonoiuaii,  Hippab- 
oHus  found  that  it  required  a  diminution  of  seven  or  tif^t 


■muMMMaXMM 


iNMMMeaWM 


LBNOTB  OF  TBS  TEAK 


207 


=  0000667;  ao  that 


expresses  the  ratio  in 
equator,  has  leas  than 
ina  from  observation, 
irth  is  not  hodiogenu- 
Be  toward  the  centre, 
inquire  how  the  earth 
r  is  if  its  whole  mass 
tance  of  the  equator 
a  the  centre  as  1  to 
traction  at  the  equator 

0  1.    The  ratio  of  in- 

1  in  this  extreme  case 
}us  elUpsoid.  We  con- 
Mth  utproachea  this 
in  denuty  toward  the 
attraction  at  the  poles 


AXIS,  OB   FBB. 
irOXBS. 

describing  tlie  ap- 
rare  shown  of  find- 
around  ihe  sphere 
of  a  year.  One  of 
iterva]  between  snc- 
38,  or,  which  is  the 
lator,  and  the  other 
me  po8iti(Hi  among 
HiPPABOHVs  found, 
th  those  made  two 
thieae  two  nMlhodB 
not  gire  ibe  iame 
Brad  ilipt  the  tei^ 
ttempliii^toooniDQt 
1  tinwi  n/t  tile  nmV 

ion  of  seven  or  ei|^t 


minutes.  He  therefore  concluded  that  the  true  length  of 
the  equinoctial  year  wa»  366  days,  6  houre,  and  about  63 
minutes.  When,  however,  he  considered  the  return,  not 
to  the  equinox,  but  to  the  same  position  relative  to  the 
bright  star  Spica  Virginis,  he  found  that  it  took  some 
minutes  more  than  366i  days  to  complete  the  revolution. 
Thus  there  are  two  years  to  be  distinguished,  the  ^opioal 
or  eqmnoctial  year  and  the  sid^eal  year.  The  first  is 
measured  by  the  time  of  the  earth's  return  to  the  eqmnox ; 
the  second  by  its  return  to  the  same  position  relative  to  the 
Stan.  Although  the  sidereal  year  is  the  correct  astronom- 
ical period  of  one  revolution  of  the  earth  around  the  sun, 
y«t  the  equinoctial  year  is  the  one  to  be  used  in  civil  life, 
^boKom  it  is  upon  that  year  that  the  change  of  seasons 
vdepends.  Modem  determinations  show  the  respective 
lengths  of  the  two  years  to  be  : 

Siderpa' year,        866*6*    9»    9*  =  366*. 26636. 
Equinoctial  year,  866*  h^  48-  46'  =  866-.24220. 

It  is  evident  from  this  difference  between  the  two  years 
that  the  position  of  the  equinox  among  the  stars  must  be 
changing,  and  must  move  toward  the  west,  because  the 
equinoctial  year  is  the  shorter.  TWs  motion  is  called  the 
precemon  ^  the  eptinomt,  and  amounts  to  about  M' 
per  year.  The  equinox  bemg  simply  the  point  in  which 
the  equator  and  the  eeliptie  intersect,  it  is  evident  that  it 
can  change  only  throu£^  a  change  in  one  «r  both  of  these 
oirolfis.  HwPAWJHTO  found  that  the  change  ^was  in  the 
equator,  and  not  in  the  ediptie,  beeanse  the  declinations  of 
the  stars  changed,  while  thrar  latitudes  did  not.*    Since 

•  To  dewribe  Am  ^eoijr  of  (he  ancient  astroaaam*  wltt  perfect 
eom^toM.  w«  ought  to  aajthfit  they  ooMldnwl  AepteMSbothof  the 
muimmAmSMto^^  tavailaUe  and  ths  notion  of  praoesirih»  to 
tediMtaadBwnviitatlonot  th«  wholeoslasltaa  i|iheN  amtad  «« 
MbotttiMitotfeMaattds.  IWs  would  iitednce  achvifi  i»  ite 
^tfttaB«f  tteaWMntallvBto  As  squator,  bol  aol  uMUt  te  d» 


'vmmiim 


!i06 


A8TR0N0MT, 


the  equator  is  defined  as  a  circle  everywhere  90°  distant 
from  the  pole,  and  since  it  is  moving  among  the  stars,  it 
follows  that  the  pole  most  also  be  moving  among  the  stars. 
But  the  pole  is  nothing  more  than  the  point  in  which  the 
earth's  axis  of  rotation  intersects  the  celestial  sphere  :  it 
must  be  remembered  too  that  the  position  of  this  pole  in 
the  celestial  sphere  depends  solely  upon  the  direction  of 
the  earth's  axis,  and  is  not  changed  by  the  motion  of  the 
earth  around  the  sun,  because  the  sphere  is  considered  to 
be  of  infinite  radius.  Hence  precession  shows  that  the 
ydirection  of  the  earth's  axis  is  continually  changing. 
Careful  observations  from  the.  time  of  Hippabchvb  until 
now  show  that  the  change  in  question  consists  in  a  slow 
revolution  of  the  pole  of  the  earth  around  the  pole  of  the 
ediptio  as  projected  on  the  celestial  sphere.  The  rate  of 
motion  is  such  that  the  revolution  will  be  completed  in 
between  25,000  and  26,000  yean.  At  the  end  of  this 
period  the  equinox  and  solstices  will  have  made  a  com- 
plete revolution  in  the  heavens. 


Th«  natora  of  thk  motioa  will  be  seen  nrare  oleailj  by  referring 
to  F^.  49,  p.  100.  We  have  there  repneented  the  earth  in  four 
poaitfons  during  ite  aiwaal  revolution.  We  have  repreeented  the  axis 
M  inclining  to  the  ri|^t  in  each  of  these  podtiona,  and  have  de- 
aoribed  it  aa  remaining  parallel  to  itaelf  durnw  an  entire  revohitioiB. 
The  i^enonena  of  preMadon  ahow  that  thia  Ii  not  abaolutely  true, 
but  tnat,  in  reality,  the  direction  of  the  axia  ia  alov^  dttogiiw. 
Tliia  change  is  aoch  that,  after  the  Iqiae  of  aone  6400  yeais,  %Sm 
north  pole  of  the  earth,  aa  repreaented  in  the  tftuty  will  aot  in- 
cline to  the  right,  but  toward  the  obeerver,  the  Mwrnnt  of  the  in- 
elination  remaliiing  nearty  the  same.  Tbe  riault  will  evidently  be 
aahiftingoftheaeaaoni.  At  D  we  dwU  have  the  winter  stris&eau 
beeanae  the  north  pole  will  be  iadined  toward  the  obaerver  and 
tlMrafore  from  the  aun,  while  at  Am  ahall  have  the  vetnai  equbwx 
Instead  of  the  i^rter  Mdatiee,  and  ao  on. 

In  0400  yeara  more  the  north  pole  will  be  incUned  toward  the 
left,  and  the  kaaaooa  wiU  be  reversed.  Another  intarval  of  the 
aame  length,  and  the  north  pole  will  be  iaellaed  tnm  the  obsorvsr, 
the  aeaaona  being  ahlfted  throagh  another  qnafthuit.  fiMlly.  ai 
die  eady  abottt  15,800  years,  the  ask  wffl  hava  rasamid  Ita  oripMd 
direction. 

Precearion  thus  aiisea  from  a  liotlMi  of  the  eaxth  akms,  aad 
not  of  the  heavenly  bodies.  AHhSlgii  tiWtaiwctio«oHheeattt*s 
axia  cbaagea,  yet  tiiepaeitkm  of  this  axis  relative  to  the  crast  <tf  the^ 


rwhere  90**  diBtant 
unong  the  stars,  it 
ig  among  the  stars, 
point  in  which  the 
selestial  sphere  :  it 
on  of  this  pole  in 
n  the  direction  of 
the  motion  of  the 
re  is  considered  to 
on  shows  that  the 
tinually  changing. 
HipPABCHVs  until 
consists  in  a  slow 
ind  the  pole  of  the 
bere.  The  rate  of 
1  be  completed  in 
it  the  end  of  this 
have  made  aoom- 


re  olflsriy  by  leferring 
ted  tlM  earth  in  four 
re  lepneMtfld  the  uie 
Mitioiu,  end  have  do- 
ff an  entire  lerolntioiB. 
le  not  abeolotely  true, 
I  is  elowly  daaiging. 
■ome  MDO  man,  iSm 
be  flgun,  will  aot  in- 
the  amount  of  the  in* 
•ndt  will  wrideatly  be 
ve  the  winter  eirisHML 
raid  the  obsenrer  and 
ire  the  re»»l  equinox 

e  inclined  towaidthe 
lother  interval  tA  the 
led  tnm  the  obaerrer, 

(?•  leMBMa  ni  onpaai 

the  easth  CkM,  aad 
llnelioB of  fhe Mirth's^ 
Aire  to  the  oniet  <rf  the^ 


iiiiiwimi 


PBEGEBaJON. 


309 


earth  remaine  inrariable.  Some  hare  rappoeed  that  pveceirion 
would  reeult  in  a  change  in  the  porition  of  the  north  pole  on  the 
Burfece  of  the  earth,  so  that  the  northern  resiona  would  be  oorerad 
by  the  ocean  h  a  remilt  of  the  different  direction  in  which  the 
ocean  would  be  carried  by  the  centrifugal  force  of  the  earth  ■  rota- 
tion. This,  howerer,  i«  a  mietake.  It  hae  been  shown  by  a  mathe- 
matical investigation  that  the  positioa  of  the  poles,  and  therefore 
of  the  equator,  on  the  surface  of  the  earth,  cannot  change  except^ 
from  some  rariation  in  the  arrangement  of  the  earth's  interior. 
Scientific  investigation  has  yet  shown  nothing  to  indicate  any  prob- 
ability  of  such  a  change.  ....  • 

The  motion  of  precnsion  is  not  uniform,  but  is  subject  to  several 
inequalities  which  are  called  Nutation.  These  can  best  be  under- 
stood in  connection  with  the  forces  which  produce  preoession. 

Oknae  of  Fiao— inn,  eto.— Mr  Isaac  Nbwtom  showed  that  pre- 
cession was  due  to  an  inequality  in  the  attraction  of  the  «m  and 
moon  produced  by  the  spheroidal  figure  of  the  earth.  If  the  earth 
weie  a  perfect  homogeneous  sphere,  the  direction  of  its  axis  would 


Vm.  48. 


never  ehahse  in  ooMeqaence  of  the  attiaetioa  of  another  body. 
BttttheexMSsef  natter  around  the  equatorial  regions  of  the  earth 
isattnwtod  by  the  eun  and  aMmn  in  swh  a  way  as  to  cause  a  tum- 
infff^mewhhsh  tends  todiaage  the  dhreetloD  of  the  axis  of  fote- 
£m.    Tte  show  tha  mode  ofaSon  of  this  foiee,  lea  us  flonsUer  the 

earth  as  a  sphere  eneirelad  tar  a  large  ri««f  «*  ■••^^«?»S' 
aionad  its  equator,  sa  in  Fig.  W.  SappoM  a  «^  •^n<*i>«^^ 
sitnsted  ift  Oe  dlnetiDB  cl^  so  that  &•  Hnes  la  f  "•»•  ^^J?"**" i* 
t  3  ifiw  are  attneted  an  Am,Bh  Ot^^,  wMeh  wiM  be  neariy 
paraQdT  The  aMmetlTa  fonM  wiU  mdoally  diminish  from  .d  to 
jTmov  to  t^g>M*v^^**»<»  <>'**>*  ^'■*^'^'*^  the  attractlag 
body.    Mk  us  pot :  " 

r.ttM  4ttstaMMof  the  (Mrtre  C  from  the  attraetfag  bodgr. 

«!  tim  ndi^  4  9  ss  S  <7  of  the  equatorial  ring,  mumBHad  1^  the 
co2ue  ottfae  angle  4  (74^  so  that  the  diatanoe  oT^  ftoia  the  attvaet- 
ing  eeam  is  r-*a,  and  Oat  of  Jl  ia  r-f  pk 

a*.  Oe  mam  «f  the  attiBotlQg  body } 


tio 


ABTRONOMT. 


m 


The  MoelerKtive  sttnotion  exerted  st  the  three  point*  A,  0,  B  will 
then  be 


m 


m 


The  radiiu  p  being  very  iinaU  compared  with  r,  we  may  develop  the 
denominators  of  the  first  and  third  fractions  in  powers  of  - 
by  the  binomial  theorem,  and  neglect  all  powers  after  the  first, 
fhe  attractions  will  then  be  approximately  ■ 


r* 


mp ,    m 


The  forces  ?^-^  will  be  very  small  compared  with  -j  on  account 
of  the  smallness  of  p. 
The  principal  force  J  will  oauM  all  p«rts  of  the  body  to  fall 

equally  toward  the  attracting  centre,  «>djrill  therefore  cause  no 
r^on  in  the  bodv  mmI  bo  dUaga  in  tbedinotioa  of  the  •^^JfS. 
Supposing  the  bocfy  to  wolve  anHmd  t^,««*"  *•  "»  °^^\7'A 
maycon<Sive  tl£ii2ttncthm  to  be  oounterbiOMioed  by  the  soHsalled 

centrifugal  forae.*  ^^ 

Subtracting  tUanBifoi«priiicipdfcm»,tli«o  la  left  a  force  -^ 

acting  on  ^  ta  the  diNetkm  Am^uAm  wi"^ '««»  •«**"»  o"*  ^^ 
the  opposite  dl*«:tloii»  A  ^\»^i^i^*^»^J^j!;!^^'*  ^"^ 
to mAVthe aarth  rotate  amad  •»  •«1»P#»«S!W^  ^^^^^ 
a  direction  aa  to  make  the  line  C il  «  cofitdde  with  (Tc,  and  ttiat, 
if  no  causemodifled  the  action  of  these  forcea,  the  earth  would  os- 
cillate back  and  forth  on  that  axis. 

•  We  may  here  mention  a  veiy  common  mtoaopwhenskm  reijecttiig 
what  is  son^timeB  called  ceptrfrugal  force,  "J^  "£P«*ft  £*  J^ 
fotoe  tending  to  make  a  body  fly  awar  from  Oie  oentra.  «*•  "^ 
SiSiSd^thebodywllllIyJwni  5»^««lS: :22i,2*!^*5S^ 
fone  eieeeds  the  centiWa,  and  •?*?»*  •*^*?«J2?*'^-«2S8d 
a  mistake,  such  a  foroe  aa  this  having  no  ezlatenoe.    t™  *^!C 

^JS%^  ia  not  pnyeriy  a  ^'''^^'«9^j!S*,Si:^^J^'Sl 

S^i^thewhWtagQyaiinrtltocenti^^ 

thltdlaw  €A  motion,  is  eoual  and  opporite  to  that  IqiM.   wmi  a  aHMie 

aary  to  make  tETstone  coostantty  deviate  from  the  rtralpht  tty^te 

■tone  offefB  to  this  deviation  to  oonaejiueBoe  id  >..iyrtl>^  _PP'.aiS 
caae  of  tiM  phmets,  tin  centrifugal  force  is  «*r  tii«  iwMaaoe  oltewfl 
^tiw  toXStSe  planet  to  tSeson'e  -ttnctfoB.  M  *•  ""WjJSSJ 
Sesk.«1tttte  sun  shouM  cease  to  attract  tiio  pianM,  *«  <«S*P*S 
^<;)Strifi»l  fowea  woohl  botii  ««•  tortantlyjjMd^tiie  i^iew 
Sanrt^oSdTin  acconlanoe  with  the  tot  kw- d  motton.  fly  f orwanl 
b  Uie  stni^t  line  to  which  it  was  moving  at  the  moment. 


p-CTWIi«CTOgjlW»W»WWitlW8*IIIWI^^ 


l>',''jr<tV'*<!' 


iiiiiliBiiiiii 


ituta:    t. 


til 


IMrfiita^0,J9wUI 


%  we  may  derelop  the 


r, 


ons  in  powers  of 


owen  after  the  first. 


id  with  -i  on  account 


of  the  body  to  fall 

ill  therefore  cause  no 
MsttM  of  the  axis  N8. 
eoBtre  in  an  orbit,  we 
aaoed  I17  the  so-called 


ero  is  left  a  force 


%mp 


ft 


fotee  Mting  on  B  in 
tlMM  two  forces  tend 
rfngthioiirii  (7  in  such 
dewith  (/«,  and  that, 
is,  the  euih  would  os- 


opnfaendon  respecting 
dis  supposed  to  be  a 
the  oeatre.  It  Is  soma- 
•  when  the  centrifagal 
0  opposite  ease.  This  is 
Jatenoa.  The  so-called 
one  at  aD.  but  only  the 
etalfarae,wfaidi,bylha 
•tfoiBe.  WhenaelOM 
siiiuily  the  fbrae  naofla- 
m  tM  straUit  Hae  la 
ke  naisluioewhidlthe 
itataiertia.  Bo.  taithe 
ly  thA  nsfataMe  offend 
OB.  If  the  sUnK  should 
^aaat,  th«  eentrlpetal 
voietf,  and  the  atone  or 
of  notioii.  lly  forwani 
hei 


But  a  modifving  cause  b  found  in  the  rotation  of  the  earth  on  its 
own  axis,  which  prevents  any  change  in  the  angle  m  C  e ,  but 
causes  s  very  slow  revolution  of  the  axis  N  8  around  the  perpen- 
dicuUr  line  O  B.  which  motion  is  that  of  precession.* 

Nutation. — It  will  liel^n  that,  under  the  influence  of  Ihe  grav- 
itation of  the  sun  and  moon,  precession  cannot  be  uniform.  At  the 
time  of  the  equinoxes  the  equator  A  Bot  the  earth  passes  through 
the  sun,  and  the  latter  lies  in  the  line  B  0  Am,  wo  that  the  small 

Ktcessional  force  tending  to  displace  the  equator  must  then  vaniiii. 
is  force  increases  on  Doth  sides  of  the  equinox,  and  attains  a 
maximum  at  the  solstices  when  the  angle  m  Ce  is  Mi".  Hence  the 
precession  produced  by  the  sun  takes  place  by  semi-annual  steps. 
One  of  these  steps,  however,  is  a  little  lunger  than  the  other, 
because  the  earth  is  nearer  the  sun  in  December  than  in  June. 

Again,  we  have  seen  that  the  inclination  of  the  moon's  orbit  to 
the  equator  ranges  from  18^*  to  98^°  in  a  period  of  18' 6  years. 
Since  the  preoessioual  force  depoids  on  this  inclination,  the 
amount  of  precession  due  to  the  action  of  the  moon  haa  a  miiod 
equal  to  one  revolution  of  the  moon's  node,  or  18*6  years.  These 
inequalities  in  the  motion  of  precession  are  termed  ntftojiM. 

Onaiisw  in  the  Bight  Aaosnaiona  and  DMUnatlona  of 
tho  Stan. — Since  the  declination  of  a  heavenly  body  is  ita  an- 
gular distMice  from  the  celestial  equator,  it  is  evident  tluit  any 
change  in  the  position  of  the  equator  must  change  the  decUnatiuas 
of  the  fixed  stars.  Moreover,  dnce  right  ascmsiona  are  oounted 
from  the  position  of  the  vernal  equinox,  the  change  in  the  position 
of  this  equinox  produced  by  precession  and  nntaniDn  must  change 
the  right  ascensions  of  the  stars.  The  motion  of  the  equator  may 
be  represented  by  supposing  it  to  turn  slowlv  around  an  axis  lyimr 
in  its  plane,  and  pointing  to  9^  and  18^  of  right  aacension.  AU 
that  section  of  the  equator  lying  within  6^  of  the  vernal  equinox 
(see  Fig.  4S,  page  108)  is  moving  toward  the  south  ^downward  in 
the  figure),  while  the  oppodte  swtion,  from  6^  to  18^  rioht  aacen- 
sion, is  moving  north.  The  amount  of  this  motion  is  80"  annually. 
It  is  evident  uwt  this  motion  will  cause  both  eouinoxea  to  shift 
toward  the  right,  and  the  geometrical  student  will  be  able  to  see 
that  the  amount  of  the  shift  will  be  : 

*The  reason  of  thisseemingparadox  ia  that  the  rotative  foroee  acting 
on  A  and  17  are  as  it  were  mttrUmUi  bgr  the  diurnal  rotatioBanund 
N8.  SiqKioea,  forounniple.  that  A  receives  a  downward  and  Jl  an  up- 
ward hnpnlae.  so  that  thqr  bq;in  to  move  in  these  directions.  At  the 
end  of  twtf  ve  hoore  A  ms  moved  around  to  B,  so  that  its  downward 
motioii  now  tends  to  iaereaee  the  aa|^  m  (7  e,  and  the  upward  motioo  of 
B  has  the  same  effect  If  wesiqipoeeaaeriesofimpnlMa,adimlBntloa 
of  the  hidiuOion  win  be  produced  daring  the  first  18  houra.  hot  after 
that  tiie  effect  of  eadi  fanpolBe  wtn  be  ooontariMJaneed  br  that  of  It 
hours  beion.  so  that  no  further  diminutioo  will  take  phwe ;  but 
everv  itagalae  wiD  produce  a  sodden  permaaentdiaage  In -the  direction 
of  theaMsJriS,  ttesadJf  movfa^  toward  and  5  fhm«  the  obaarver. 

This  same  law  of  rotathm  ia  exemiriified  hi  the  ajfroecope  and  the 
chOd'a  top,  eadi  of  whidi  are  kept  ereot  by  the  mmkn,  thMgh  grav- 
ity tsmklo  make  thsm  ftlL 


mm 


ABTRONOUr 

On  th«  equator,  20"  cot  w ; 

On  the  ecliptic,  20*  coMC  M ;        .    .      ^^..^     ,  «„ 

u  being  the  obliquity  of  the  ecliptic  (88"  274').  In  c<.n«equence, 
the  riSt  ascension,  of  sUrs  near  the  equator  are  consUntly  inoreaa- 
inabf  about  46"  or  arc,  or  8«.07  of  tlilrt- annually.  Away  from 
thi  equator  the  increase  will  vary  in  amount,  because,  owing  to  the 
motion  of  the  pole  of  the  earth,  the  point  in  which  the  equator  to 
interN»ted  by  the  great  circle  pasdng  through  *»«  PoJ  "jj  [J* 
star  will  vary  as  well  as  the  equinox,  it  being  remembered  that  the 
ri^t  ascenrfon  of  the  star  to  the  dtotance  ofthto  point  of  interseo- 

"•CSeJ?  rijhJrical  trigonometry  will  find  It  «.  Improving 
exeretoe  to  work  out  the  formS.  for  the  annual  change  in  tfie  right 
Mansion  and  declination  of  the  stars,  arising  from  *>>«  "otJon  »' 
ST  equator,  and  consequently  of  the  equinox.  He  wiU  find  the 
remit  to  be  ss  follows  :  Put 
n,  the  annual  angular  motion  of  the  equator  («0  W), 
«,  it«obliqut7(l8'»r.8),  ,♦»...♦,. 

a  »,  the  riffhc  ascension  and  declination  of  the  sU  , 
Then  we  whaU  9nd :  ,       ^     j 

Annual  change  in  R.  A.  =  n  cot  «  +  n  sin  a  tan  *. 
Annual  change  in  Deo.  =  n  cos  a. 


7|').  In  cunRequ«nce, 
•re  consUntly  inorcM- 
uiniuUy.  Awsy  from 
becauM,  owing  to  the 
n  which  the  equator  is 
i>ugh  the  pole  and  the 

P  remembered  that  the 
thia  point  of  inteneo- 

11  find  it  an  improving 
ual  change  in  the  right 
ing  from  the  motion  of 
loz.    He  will  find  the 

or  (20*  06), 

f  the  ata  ; 
n  a  tand. 


CHAPTER  IX. 

CELESTIAL  MEASUREMENTS  OF  MASS  AND 
DISTANCE. 

8  1.    THB  OBiaBTIAL  SOAM  OF  UMAMTSBMMMKT. 

Thr  unite  of  length  and  maw  eniploytd  by  agtronomer* 
are  necewarily  different  from  thoae  uwd  in  daily  Me. 
For  instance,  the  diatancea  and  magnitudes  of  tho  heavenly 
bodies  are  never  reckoned  in  miles  or  other  terrestrial 
measures  for  astronomical  purposes ;  wlien  so  expressed 
it  is  only  for  the  purpose  of  making  the  subject  clearer  to 
the  general  reader.     The  unite  of  weight  or  mass  are  also, 
of  necessitv,  astronomical  and  not  terrestrial.     The  maaa 
of  a  body  may  be  expressed  in  terms  of  that  of  the  sun 
or  of  the  earth,  but  never  in  kilograms  or  tons,  unless  m 
popular  language.    There  are  two  reasons  for  this  wxune. 
One  is  that  in  most  cases  celestial  distances  have  fiwt  to 
be  determined  in  tenns  of  some  celestial  unit— the  earth  s 
distance  from  the  aun,  for  instance— and  it  is  more  con- 
venient to  retain  thia  unit  than  to  adopt  a  new  one.    The 
other  is  that  the  values  of  celestial  diatances  in  terms  of 
ordinary  terrestrial  tmito  are  for  the  most  part  extremely 
uncertain,  while  the  corresponding  values  in  agronomical 
unite  are  known  with  great  Monracy. 

An  extreme  instance  of  this  is  afforded  by  the  dmien- 
siona  of  the  solar  system.  By  a  long  and  continued  seriea 
of  astronomical  observatloBa,  investigated  by  means  of 
Kbplmi's  Utwa  and  the  theory  of  gravitation,  it  is  poMMe 
to  determine  the  forma  of  ^  plMie»«|i  «Wt%  tl^r 
poaitions,  and  th^  dimensiona  in  terriit^  the  earth  » 


JBMl 


214 


ABTRONOMT. 


mean  diiitance  from  the  sun  m  the  unit  of  meaHiiro,  with 
great  preciBion.  It  will  be  remembered  that  Kki-  kk'm 
third  law  enablufl  us  todetennino  the  mean  diHtAiieu  uf  a 
pbinet  from  tlio  Bun  when  we  know  ita  period  of  revolu- 
tion. Now,  all  the  major  planets,  aa  far  out  as  Saturn, 
have  been  obaerved  through  bo  many  revolutionB  that  their 
periodic  times  can  be  determined  with  great  exactness— in 
fact  within  a  fraction  of  a  millionth  part  of  their  whole 
amount.  The  moi-e  recently  discovered  planets,  Urantu 
and  N^ptwMy  will,  in  the  course  of  time,  have  their 
periods  determined  with  equal  precision.  Then,  if  we 
square  the  periods  expressed  in  years  and  deeimnls  of  a 
year,  and  extract  the  cube  root  of  this  square,  we  have  the 
mean  distance  of  the  planet  with  the  same  order  of  pre- 
cision. This  distance  is  to  be  corrected  slightly  in  conse- 
quence of  the  attractions  of  the  pUnets  on  each  other,  but 
these  corrections  also  are  known  with  great  exactncBs. 
Again,  the  eccentricities  of  the  orbits  are  exactly  deter- 
mined  by  careful  observations  of  the  positions  of  the  plan- 
ets during  successive  revolutions.  Thus  we  are  enabled  to 
make  a  map  of  the  planetary  orbits  which  shall  be  so  ex- 
act that  the  error  would  entirely  elude  the  most  careful 
scmttny,  though  the  map  itself  should  be  many  yard*  in 
octent. 

On  the  scale  of  this  same  map  we  could  Uy  down  the 
magnitudes  of  the  planets  with  as  much  prednon  m  our 
instrumento  can  measure  thdr  anguhr  semi-diameters. 
Thus  we  know  that  the  mean  diumeter  of  the  sun,  m  seat 
itWD.  the  earth,  is  82\  henoe  we  deduce  from  lormul» 
^ven  in  conneetioB  with  pandbx  (Chapter  I.,  §  9)»  thai 
the  diameter  of  the  son  is  -0098088  of  tbe  diatanoe  «f  the 
sun  from  the  earth.  We  ean  thwefore,  on  our  WKpfeaeA. 
map  of  the  iralar  system,  ky  down  the  snnr  in  ita  true  rise, 
aoooidiBg  to  the  sdale  of  Uie  map,  horn  data  given  i&ftf&j 
by  obaervntion.  In  the  aame  way  we  cin  do  this  f<^  e«^ 
of  the  planets,  the  earth  and  moon  excepted.  Tb^m^ 
noimniediate  and  direet  way  of  finding  hot^  large:  tie 


vxmm 


MHiPKMiiS^M 


mmm 


lit  of  measure,  with 
ored  that  Kki-  kk'm 
meaii  (liBtaiicu  uf  u 
*»  period  of  ruvolu- 
far  oat  as  StUum^ 
'evolutioiu  that  their 
I  great  exactnew— in 
IMrt  of  their  whole 
«d  planets,  Uranut 
of  time,  have  their 
igion.  Then,  if  we 
s  and  deciinnU  of  a 
square,  we  have  the 
)  same  order  of  pro- 
ed  slightly  in  conse- 
ts  on  each  other,  but 
ith  great  exactness. 
B  are  exactly  deter* 
[MMitions  of  tiie  plan- 
bos  we  are  enabled  to 
irhich  shall  be  so  ex- 
ido  the  most  careful 
tld  be  many  yard*  in 

could  lay  down  the 
ncU  predsion  m  our 
alar  semi-diameters. 
Br  of  the  ran,  a*  teet^ 
ledttce  from  lormuliB 
Chapter  I.,  8  9),  thai 
}f  tiie  cUitanoe  of  tiia 
sre,  on  our  tmppemA 
e  miL  in  iti  true  iriie, 
m  data  given  ^i«elhr 
seindothisloreiw 

exoepted.  Tksm^ 
)ding  how  >rg«  tk>B 


CBLK8TIAL  MEA8URE8. 


tlB 


uarth  or  moon  would  look  from  a  ])laiioii;,  lionoe  the  ox- 
(^tiptiuii. 

But  without  further  spociHl  rosoarchJutu  thin  subjoot, 
wu  shall  know  nothing  about  the  »ade  of  our  map.  It  is 
dear  that  in  order  to  fix  the  distances  or  the  magnitudes 
of  the  planets  according  to  any  terrestrial  standard,  wo 
must  know  this  scale.  Of  course  if  wo  can  learn  either 
the  distance  or  magnitude  of  any  one  of  the  planets  laid 
down  on  the  map,  in  miles  or  in  semi-diameters  of  the 
earth,  we  shall  be  able  at  once  to  find  the  scale.  But  thir 
process  is  so  difficult  tluit  the  general  custom  of  astruoo  • 
men  is  not  to  attempt  to  use  an  exact  scale,  but  to  employ 
tiie  mean  distance  of  the  sun  from  the  earth  as  the  unit  in 
celestial  measurements.  Thus,  in  astronomical  language, 
we  say  that  the  distance  of  Mercury  from  the  sun  io 
0.887,  that  of  Vmm  0-723,  that  of  Mar$  LfiiS,  that 
otSaiiwm  9 '680,  and  so  on.  But  this  gives  ns  no  in- 
formation respecting  the  distances  and  magnitudes  in  terms 
of  terrestrial  measures.  The  unknown  qnantitiea  of  oor 
map  are  the  magnitude  of  the  earth  on  the  soale  of  the 
map,  and  its  distenco  from  the  sun  in  terrestrial  units  of 
length.  Oould  we  only  take  up  a  point  of  observation 
from  the  sun  or  a  planet,  and  determine  exactly  the  anga> 
lar  magnitude  of  the  earth  as  seen  from  ti>at  point,  we 
should  be  able  to  lay  down  tlie  earth  of  our  map  in  ito  cor- 
rect sice.  Then  since  we  already  know  the  siae  of  the 
effth  in  terrestrial  units,  we  should  be  able  to  find  the 
soale  ol  our  map,  and  thenoe  the  dimensi<ma  of  the  whole 
system  in  terms  of  those  units. 

It  will  be  seen  that  what  the  aatraiMmier  raaUy  wants  is 
not  so  mueh  die  dimenatons  of  the  solar  system  in  miks  as 
to  express  the  liae  of  the  earth  in  oekatiil  roewnres. 
Theae,  however,  Moonnt  to  the  same  tUog,  beeante  hav. 
ing  !BMS  the  oHmt  can  be  readily  dednoed  tnm.  the  known 
maa^tnde  of  the  eM^  in  twrpatrial  mearaves. 

&  migidtnde  of  tlMeafth  ia  not  the  <mly  onlmown 
qnumtHj  <m  onr  map.    jj^rom  Kanwa'a  laws  we  ean  de- 


msm 


216 


ABTRONOMT. 


termine  nothing  respecting  the  distance  of  the  moon  from 
the  earth,  because  unless  a  change  is  made  in  the  units  of 
time  and  space,  they  apply  only  to  bodies  moving  around 
the  sun.  liVe  must  therefore  determine  the  distance  of 
the  moon  as  well  as  that  of  the  sun  to  be  able  to  complete 
our  map  on  a  known  scale  of  measurement. 

S  a.    MEASUBBS  OF  THE  SOIJkB  PAKAT.T.AT. 

The  problem  of  distances  in  the  solar  system  is  reduced 
by  the  preceding  considerations  to  measuring  the  distances 
of  the  sun  and  moon  in  terms  of  the  earth's  radiiu.  The 
most  direct  method  of  doing  this  is  by  determining  their 
respective  parallaxes,  which  we  have  shown  to  be  the  same 
as  the  earth's  angular  semi-diameter  as  seen  from  them. 
In  tlie  case  of  the  sun,  the  required  parallax  can  be  de- 
termined as  readily  by  measuring  the  parallaxes  of  any 
of  the  planets  as  by  measuring  that  of  the  son,  because 
any  one  measured  distance  on  the  map  will  give  us  the 
scale  of  our  map.  Now,  the  planets  Ventu  and  Mars  oc- 
casionally come  much  nearer  the  earth  than  the  sun  ever 
does,  and  their  parallaxes  also  admit  of  more  exact  meas- 
urement. The  parallax  of  the  sun  is  therefore  determined 
not  by  observations  on  the  sun  itself,  but  on  these  two 
planets.  Three  methods  of  Ending  the  sun's  pandhuc  in 
this  way  have  been  applied,    lliey  are : 

(1.)  Observations  of  Fmim  in  transit  aorofls  the  sun. 

(2.)  ObsOTvationB  of   tiie  declination  of  Mara  from 
widely  separated  stations  on  the  earth's  nirfaoe. 
'    (8.)  Obt^vations  of  the  right  aMension  of  Jforv,  near 
the  tinMB  of  its  rising  and  setUng,  at  a  ringle  btation. 

Solar  VKral]axlhiiiiTraiiaita«rV«iva.— The  genval 
principal  of  the  method  of  determiniiig  the  pMallax  of  a 
planet  by  mmultaneons  obeervationa  at  diatant  atatfons 
will  be  seen  by  referring  to  Fig.  18,  p.  40.  If  «irQ  «!»• 
aervem,  utnatiBd  at  S  and  /S*,  make  «  nntritaanMM  «b* 
aervation  of  the  direotioii  of  th»  body  P,  it  ia  Mffciwt 


■Mjj,i^ai'J.satiaJlfflWWWi>35gJffiWm?W'-^^ 


!e  of  the  moon  from 
nade  in  the  units  of 
dies  moving  around 
aine  the  distance  of 
be  able  to  complete 
noent. 

iB,  FABALIiAZ. 

ar  system  is  reduced 
asuring  the  distances 
earth's  radins.  The 
yy  determining  their 
>hown  to  be  the  same 
as  seen  from  them, 
parallax  can  be  de- 
e  parallaxes  of  any 
)f  the  son,  because 
lap  will  give  us  the 
VemM  and  Jdars  oc- 
h  than  the  sun  ever 
of  more  exact  meas- 
theref  ore  determined 
If,  but  on  these  two 
the  sun's  parallax  in 
ro: 

u»it  across  the  sun. 
ition  of  Mart  from 
I's  surface. 

en»ion  of  Jforf,  near 
a  aingle  bCa^on. 
''•Bua.— The  gemnd 
^sg  the  parallax  <iC  a 
■  at  dittwt  Bti^iiM 
(,  p.  4e.  If  Iwo  «*- 
8  a  f^dtanpMi  •b> 
ody  P,  it  k 


mm 


TRANSn'S  OF  VENUS. 


217 


that  the  solution  of  a  plane  triangle  will  give  the  distance 
of  P  from  each  station.  In  practice,  however,  it  would 
be  impracticable  to  make  simultaneous  observations  at 
distant  stations,  and  as  the  planet  is  continually  in  motion, 
the  problem  is  a  much  more  complex  one  than  that  of 
simply  solving  a  triangle.  The  actual  solution  is  effected 
by  a  process  which  is  algebraic  rather  than  geometrical, 
but  we  may  briefly  describe  the  geometrical  nature  of  the 
problem. 

Considering  the  problem  as  a  geometrical  one,  it  is  evi- 
dent that,  owing  to  the  parallax  of  Venus  being  nearly  four 
times  as  great  as  tliat  of  the  sun,  its  path  across  the  sun's 
disk  will  be  different  when  viewed  from  different  points  of 
the  earth's  surface.  The  further  south  we  go,  the  further 
north  the  planet  will  seem  to  be  on  the  sun's  disk.  The 
change  will  be  determined  by  the  diferenee  betwera  the 
parallax  of  Veniu  and  that  of  the  sun,  and  this  makes  the 
geometrical  explanation  less  simple  than  in  the  case  of  a 
determination  into  which  Only  one  parallax  enters.  It 
will  be  sufficient  if  the  reader  sees  that  when  we  know  the 
relation  between  the  two  parallaxes — ^when,  for  instance, 
we  know  that  the  parallax  of  Venus  is  3*78  times  that  of 
the  sun — ^the  observed  displacement  of  Venus  on  the  sun's 
didE  will  give  us  both  parallaxes.  The  "  relative  paral- 
lax," as  it  is  called^  jnOl  be  9*78  timet  tiie  sun's  parallax, 
and  it  is  on  this  aione  f}iil  t!ie  disptaeement  depends; 

Thb  algebraic  procew,  wUch  is  tiiat  actually  inployed  in  the 
■olution  of  astrmioaiieal  proldeaw  of  tbis  claM,  Is  as  follows  : 

Baoh  obaenrer  is  supposed  «o  know  bk  kmgitiide  and  lati- 
txa»f  and  to  have  aaad*  <nm  .<w  asore  obswratiaui  of  the  angular 
distuee  of  tiie  oentre  of  the  ]da9|et  from  tlie  oentie  of  the  ton. 
To  work  up  tiM  obsenwtbnii' the  investigatOT  muat  have  an 
tmktmtri$  of  Vmm  and  of  Oe  ran— tinat  it,  a  Jable  ghrilig 
W)  iif(tA  ascension  and  darilaartim  of  eaob  body  hem  boor  to  boor 
as  caicubrted  turn  A»  best  aitwww laical  data.  The  epbenMris  can 
never  be  ooMldwid  dMobitaly  oevMct,  bat  Its  enw  nuqr  be  sa- 
mnnei  as  ewMtaat  for  an  entita  dav  or  nMwe.  ^  means  of  it,  the 
rj^asfeenniion  and  deeHnatjwt  of  the  j^wiet  and  of  the  aan,  as  seen 
frtii  tte  oMtee  ol  the  eariii,  mif  be  eoriumted  at  ain  ttme. 

'  le^Meslha.aMmeats  <lttoohservawens  to  Qreen- 


218 


ABTRONOMT. 


wich  mean  time,  or  the  mean  time  of  any  other  meridian.  Let 
those  mean  times  for  the  obeerver  8i  be  called  7'i,  7«,  T%,  etc. 
Suppose  that  at  these  mean  times  he  has  observed  the  distances  of 
the  centre  of  Vmvt  from  that  of  the  txxu  to  be  2>i,  Dt,  A,  etc. 
The  corresponding  geocentric  distances  are  klien  computed  from 
the  ephemeris  for  these  same  times,  7*1,  Tt,  Ti,  etc.  If  the  ephem- 
eris  and  the  observations  ivere  perfectly  correct,  and  if  there  were 
no  parallax,  these  calculated  diirtances  would  come  out  the  same  as 
the  observed  ones.  But  this  is  never  the  case.  It  is  therefore 
necessarr  to  calculate  what  effect  a  change  in  the  right  ascension, 
declination,  and  parallax  of  the  sun  and  kSmmm  will  have  upon  the 
calculated  distance.  In  this  operation  these  changes  are  considered 
as  infinitely  small,  and  the  process  used  is  that  of  differentiation. 
Let  us  put : 

a,  i,  )r,  the  right  ascension,  deoUnation,  and  parallax  of   FmtiA 

a*,  d',  ir',  the  same  quantities  for  the  sun. 

A  a,  A  4,  ^o^,  ^  S,  the  oorrections  necessary  to  the  values  of  the 
quantities  :  a,  d,  a',  and  6  in  the  ephemeris. 

di,  dt,  dt,  etc.,  the  calculated  geocentric  distances  of  V<mu$  from 
the  sun*s  centre. 

Then,  the  corrected  calculated  distances,  which  we  shall  call 
l/if  Ift,  D'l,  etc.,  will  be  expressed  in  equations  of  the  form  : 

<li  +  a.  A  a  ■!■  «',  A  a'  -f  5i  A  4  +  i',  A  d*  +  «i  » -(■  «'i  •r'  =  D*. ; 
<fi  +  a<Aa  +  a'«A<<'+iiA4+&'t  ^4'+  ei«r  -f  «'t ^r' =  D t. 

'  In  these  equations  d\,  it,  etc.,  and  the  coefficients,  at,  «i,  a*,  etc, 
to  e*!,  are  all  known  qusnnties,  being  the  direct  reralts  of  odcula- 
tion,  while  A  a,  Aa,  Ad,  and  Ad  are  unknown  oorrections  to  the 

ahemeris,  and  w  and  v'  are  the  parallaxes  of  Vmm  and  the  son, 
»  unknown,     ffi,  D**,  etc.,  are  therefore  also  to  be  Ktgaided  as 
unknown. 

But  when  all  corrections  are  allowed  for,  these  eometed  calcu- 
lated distances  Jft,  2X|,  etc.,  ought  to  be  the  same  as  the  observed 
distances  1/t,  If*,  etc.,  which  are  known  ouantitiM,  being  tiie  direct 
result  of  observations.  So  if  we  put  Jh  lor  D'l,  etc.,  and  transpose 
A  to  the  other  dde  of  the  eqnatlaa,  and  porfonn  the  sane  prooeas 
on  the  other  equations,  we  shall  have : 

«iAa  +  a'|Aa'-|>tiAd4-VtAd'-f«i)r+«'i«'saJ>i  —  <ii 

These  equationa  admit  of  htimt  modi  slmpMed.    If  we  mppim 

•ad  r«Hw  ohAaged  l^  the  atiM  sMNut 


the  right  ascensions  of  the __  _ 

-this  is,  if  we  suppose  A«'  s  A4l  tt  b  evidSit  tiSi*  tiMl^  fttitMMMs 
will  main  sttbslaiitidlyiiBalterwi  la  gidtt  that  tUa  iMy  Iw  4*a« 
in  the  equations,  we  vast  lMiv« 


«»  «—•'!, 


beoauie  the  real  ehaiigawfll  be,  in  tiw  ew*  anppessd, 
«,  A^a  4.  «*!  A  <r  as  («,  4.  a',)  A  a  s  0. 


■^.•,'nxi.smmia 


my  other  meridUm.    Let 
e  called  Tt,   T.,  T„  etc. 
observed  the  difltances  of 
iiu  to  be  2)>,  Bt,  Dt,  etc. 
are  klien  computed  from 
',,  T,,  etc.   If  the  ephem- 
correct,  and  if  there  were 
)uld  come  out  the  tame  as 
he  caie.     It  ia  therefore 
ee  in  the  right  ascenrion, 
T«nu«  will  have  «?»"  *^ 
eae  changes  are  considered 
s  that  of  differenUi|tion. 

and  parallax  of   Venui. 

BMsiy  to  the  Talues  of  the 

ic  distances  of  Venw  from 

nces,  which  we  shall  cafl 
quadons  of  the  form  : 

i'  +e,it  +  e'tw'  =  iyy, 
ii'  +  Ci  ir  +•  c'l  jr*  =  D  ». 

)  coefficients,  at,  «i,  «•»  etCM 
he  direct  results  of  calcula- 
nknown  oorreetions  to  the 
utes  of  Ymiu  and  the  ran, 
sfoi«  also  to  be  regarded  as 

for,  these  corrected  calcu- 
be  the  same  as  the  observed 
I  Quantititis,  being  the  direct 
.  for  D-,,  etc.,  and  tnaspose 
1  porfwm  the  same  prooess 

«,  ir +  «'!«'  = -Di  ■- <*» 

e,r  +  «'•«'=»  A  — *i  •**• 

liabnpliied.    U^t»Ppim 
ii^iiBffed  l^  the  MHpM  iMMMBt 

I  flidflr  tbrt  fbia  oHqr  t>*  «»• 


RiqWOMd, 
a',)  A  a  a>  0. 


TRAN8IT8  OF  VENU8.  819 

In  the  same  way,  we  must  have  very  nearly, 

h'l  =  —  J, ;  c'l  =  —  c. 

Then  if  we  substitute  these  values  of  the  accented  coefficients,  the 
first  equation  will  be : 

ai  (A  a  —  A  a')  +  *i  (  A  «*  —  A  iJO  +  «'  ("f  —  TO  =  ^'  —  **'• 
If  we  put  tat  brevity, 

«a=Aa— Ao';  y=Ad— Arf', 
the  equations  will  become  : 

oi «  +  *i  y  +  «!  (t  —  wO  =  ^'  —  t'l 

The  parallaxes  of  the  sun  and  Veniu,  it'  and  ir,  are  inversely  as  the 
distances  of  the  respective  bodies  from  the  eartii.  During  the  tran- 
sit of  December,  1874,  these  distances  were : 

Distance  of  son,      0-0847, 
"        "    FmtM,  0-2644. 

So^  if  we  put  ir«  Ust  the  parallax  at  distance  1,  we  shidi  have: 


Actual  parallax  of  the  son,  it'  = 


Actual  parallax  of  Vemu,    it  = 


0-9847 


=  l-0165>r.. 
=  8-7892  If.; 


Whence 


0-8044 

ir-ir'=sa.7e«7ir.. 

Sabstitating  this  value  in  our  equationa,  they  will  beoone : 

at  • -I- fti  y -I- S-7007  «i  «•  s  i>,  —  d, 
at*  +  h%f  -f  S>7667 e* «•  a^J),  —  <^  etc 

AU  the  coneqwading  eaostkns  bdng  foroMd  in  tUs  way,  flmn 
the  observatimis  at  the  various  statioB%  their  solotkm  will  ^ve  the 
vahiea  <rf  Hie  three  imlmown  qnawtitiea,  m,  y,  aadirt.  Ilie^valtie  of 
w,  win  hi  tiM  pMalluc  odnvspoiMltog  to  the  astnmmnkal  vbH^ 
that  ia,  tin  anUar  awnl'illiintiir  eT the  eatth  taNi  at  the  mean 
cUs^mee  llni  «M  Mu. 

HlWk  tmuf  oliaanallun  HiriBKla,  we  hav«  nore  •quatioBa  than 
thw  mm  MjpMwmsMMitMi*  t»  tt  datiTmliiad,  V  i^  Oy  eqnttiooa 
wiM  Ma«b(pM*M^«MKM^^><«#^^  and  eoold 

reJiMt  mj  af  flw  aamliia  mm  lirHhant  aia#N«  til*  mndt.  Bat 
daoi  mA  aqmiOoa  ft»aiMai4^  alleetad  Hrlth  eqon  of  «beerv»- 
Oam,  «b»  MwWeM  puj-tia  to  «*  !•  toobtafca  «M»«*miM»I« 
vatow  of  -Uo  — luwwwl-.  qjiiWi(|tai,.fcQo>  the  oombfaatloii  ^  «&  the 
equatlooi.  tiMMa  tNAila^  mm  '-mm  mbkkk  iwder  tha  mm-'  of  A« 
sqaaiw  of  ttw-Btataiiiltig  oiMn  of  ellseMMrtfcpi-^  (or,  nriiMr,  of 


mm 


ASTRONOMT. 

we  substitute  ia  the  wiuation 

1  «  In  ffcnerftl  the  cquntlon  will 
any  a"«m»d;'»»T*"!h«iwm  wmaJn  a  small  difference  between 
not  be  satisfied,  »»«*  Jf"  T'J^fjSu,.  Let  us  caU  A.  the  dUIer- 
the  two  'n«"»]T'\K''**  n^  w^W  the  second  equation,  A,  from 
enee  obtained  ^^ ^^^ ^mS v^sZ the  «mot  thesq«a«.of 
the  third,  and  so  on,  and  let  us  pu*  o 
these  quantities,  so  that 

S=  A«,  +  A»,+ A%  +  elc. 

Then,  for  e«.h  svjem  of  vaj- of  ^^-^Jj'  o^^^d  '^^ 
««ume,  there  will  be  •  ^'^^af  wWch  makes  S  the  lew*- ,^ 
probable  system  of  '«^»«»  T^"  Siti"  "W'*'*^  *"  ^^^  ***  ""^ 
•^Themotiiod  by  which  5*"  "^Vortaon  astronomical  compu- 
^  bMt  $qvam,  and  is  developed  in  worns  on  » 

be^t^SJ  from  '^"l^^^  ^^^  Sb  :tV^^  on.  in  the 

-crthrot^r^^^ 

determines  the  declination  ^JJ^£*%i^  declfnationswill  be 

moment  of  transit  over  hie  ™»™°:     *':'^"- w«<«  the 

■uumvu*  _i..i~  amnnnt  of  nan 


s'c;^i:^;«'tin«athr^jtjj^^^ 

oeiMimlW  about  a  couple  of  montM.  /uiy  "JSfawidjle  ooea  •» 
S?be  chSen  for  tbS.  I«'P«^,J"LXK?  BhSd  th«  pb««t 
3Se  when  the  Pl«;l*«  "TlTtlMfS^^  **•  .^««S 
be  exactly  at  its  Pfri^^,  •*JSfJS7  iXSwhSion  it  would 
from  the  Sarth  would  Jf- «2LS^ii£'to  tiS  «25S«^ 
he  0.68.    TWs  great  dlllerwiee  U  owing  »;^™T    gk-driMt  Wg.  *8« 

p.ll5,whichglTesapl«iofnortofttJwow      ^^^  ^ 

fee  fivorable  oVfo^^^^l^^^SfSiS^^^ 
waathatofl8W,w1iichg»w«»"»of"*JJ!^rrr^  TM« 

^ba  was  8-.577.  and  «»  "2*2222gi*iSl*-«d  to  allow 

great  as  tills.     ^        .,  in      t   ..^ifit-^-**^-**  *— ^** 

of  8q>tffBb«r  WM^LTSi SnJafiwJ^ *>»  "*^^ 


)li8cnr«l  quantities  and 
r  instance,  suppose  that 


-cneral  U>e  equation  will 
small  difference  between 
Let  us  caU  ^t  the  diiler- 
lecond  equation,  At  iiom 
the  sum  of  the  squares  of 

I-  etc.  ! 

id  If.,  which  we  choose  to 
ralue  of  S,  and  the  most 
ich  makes  B  the  lewt. 
ached  is  called  the  fMthod 
i  on  aatronomical  compo- 

Kan.— This  paralUz  may 
owa,^  Inthatiu^^ly 
,  of  bhMrrers,  one  in  the 
lemisphew,  ewsh  of  whom 
rtfromdaytodayatthe 
rhese  declinattons  will  pe 
iacdi«efencebetweeii«» 

Iff.  18,  p. «.  Th«  *••!!?" 

[to  the  *»j^jj^;y«; 


PARALLAX  OF  MAM8. 


Furallax  of  Man  in  Bight  ABoenaion.— Another  method 
of  measuring  the  parallax  of  Man  is  founded  on  principles  entirely 
different  from  those  we  have  hitherto  considered.  In  the  latter, 
observations  have  to  be  made  bv  two  observers  in  opposite  hemi- 
spheres of  the  earth.  But  an  observer  at  any  noint  on  the  earth's 
surface  is  carried  around  on  a  circle  of  latitude  every  day  by  the 
diurnal  motion  of  the  earth.  In  conse<}uence  of  this  motion,  there 
must  be  a  corresponding  apparent  motion  of  each  of  the  planets  in 
an  opposite  direction.  In  other  words,  the  paralhix  of  the  olanet 
must  be  different  at  different  times  of  the  day.  This  Aumal 
change  in  the  direction  of  the  planet  admits  of  being  measured  in 
thefoUowing  way :  The  effect  of  paralkuc  is  always  to  make  a 
heavenly  body  appear  nearer  the  horimm  than  it  would  appear  as  seen 
from  the  centre  of  the  earth.  This  will  be  obvious  if  we  reflect 
that  an  observer  moving  rapidly  from  the  centre  of  the  earth  to  its 
circumference,  and  keej^ng  his  eye  fixed  upon  a  planet,  would  seie 
the  planet  appear  to  move  in  an  opposite  direction — ^that  is.  down- 
wwa  relieve  to  the  point  of  the  earth's  surface  which  he  umed  at. 
Hence  a  planet  rising  in  the  east  will  rise  later  in  consequence  of 
paraUaz,  and  will  set  earlier.  Of  course  the  rising  and  setting 
cannot  be  obawved  with  sufficient  accuracy  for  the  purpose  of 


parallax,  but,  rince  a  fixed  star  has  no  parallax^ 
the  planet  relative  to  the  stars  in  its  neighborhood  will  change 
during  the  intervallMtween  the  rising  and  setting  of  the  planet 
The  observer  therefore  determines  the  positon  of  Mart  relative 
to  the  Stan  surrounding  him  shortly  after  he  rises  and  aj^in 
shortly  before  he  sets.  The  observations  are  repeated  night 
after  night  as  often  as  poarible.  Between  each  pair  of  east  and 
west  observations  the  pbmet  will  of  course  change  its  podtion 
among  the  staiB  in  consequence  of  the  orirital  motions  of  the 
earth  and  planet,  bat  these  motions  can  be  calcukted  and  allowed 
for,  and  the  changes  still  outstanding  will  then  be  due  to  paralhu. 

The  most  fliTOiwle  regions  for  an  observer  to  determine  the  p«r- 
idlax  ia  tbJs  way  we  those  near  the  earth's  equator,  because  he  is 
thoie  oarried  around  on  the  lamst  circle.  If  he  is  nearer  the  poles 
than  the  equator,  the  cirde  willbe  so  smalt  that  the  parallax  wul  be 
hardly  worth  determininff,  while  at  the  poles  there  will  be  no  paiu 
allaene  elnnge  at  all  of  ttie  kind  hni  described. 

AppHoations  of  this  mMhod  oaTe  not  been  very  numerous, 
althom^  H  waa  ouggested  b9  ThUumaD  neariy  two  centuries  ago. 
The  lalMt  and  BHMt  aoeeeasflu  tiki  of  it  was  made  by  Mir.  Datid  Oiu. 
of  BffgHiMJ  daring  the  oi^oaiti(m  <rf  Mtrt  in  1877  above  described. 
The  p^t  ot  obaMrvatiofi  dioaen  by  him  waa  the  idand  of  Aaeen- 
skNi,  wMt  of  Afrioa  and  near  the  eqiMtor.  Hla  meaqires  indlei^ 
a  euMMonibla  fodiietioa  in  the  wewflyreedved  valoes  of  the  vt 
panUix,  and  an  inerease  in  the  dlatanoe  of  the  sun,  makinj, 
htter  ooBM  somewhat  nearer  to  the  old  vahie. 

MioBmntgr  of  Ham  PitwmiiiaWoni  of  BeHar  PawllMc 

TIm  pttalbx  of  JUNi  at  oppoaitioii  k  nrely  moro  ihaa 


'«im 


322 


ABTBONOMT. 


aO',  and  the  relative  parallax  of  Venm  and  the  ron  at  the 
tune  of  the  tmnait  is  lew  than  24'.     These  qnantitiea  are 
w>  nnaU  as  to  ahnoat  elude  very  preoiw  meaaurement ;  it 
iB  haidly  poarible  by  any  one  set  of  measnree  of  jw^ 
to  determine  the  latter  without  an  uncertainty  of  ^^  of  its 
whole  amount.    In  the  distance  of  the  nm  this  corre- 
sponds to  an  uncertainty  of  nearly  half  a  miUion  of  miloa. 
ABtronomeiB  have  therefore  sought  for  other  methods  of 
determining  the  sun's  distance.    Although  some  of  ttese 
may  be  a  Uttle  more  certain  than  measures  of  pwrillax,  th«re 
is  none  by  which  the  distance  of  the  sun  can  be  detenuined 
with  any  approximation  to  the  accuracy  wWch  character- 
izes other  celestial  measures. 

Other  Methods  of  DetMnnininc  Sotar  *««"«-~;^ 
Ycry  interesting  and  probably  the  most  accurate  method 
of  measuring  tiie  sun's  distance  is  by  using  Kght  as  a  nwfr 
genaer  between  tiie  sun  and  the  earth.    We  shall  hereafter 
see  in  the  chapter  on  aberration,  that  the  time  reqmred  for 
light  to  pass  from  tiie  sun  to  tiie  earth  is  known  witii  con- 
rfdenble  exactness,  being  very  nearly  4»8  seconds.    If 
then  we  can  detennine  experimentally  how  many  miles  or 
kilometrea  light  moves  in  a  second,  we  shall  at  once  have 
tiie  distance  of  the  sun  by  multiplying  that  quantity  by 
498     But  the  velocity  of  light  is  about  800,000  falometres 
ner  s*eond.    This  distance  would  reach  about  eight  times 
iroundtheeartii.    It  is  nmjly  possible  tiiat  two  pomts  on 
tiie  eartii's  surface  more  than  a  hundred  kilometrea  apui 
are  visible  from  each  other,  and  distinct  vision  at  distenoes 
of  more  tiian  twenty  kilometres  is  rare.    B^******' 
mine  experimentdly  tiie  time  required  for  Ui^t  to  pus 
between  two  terrestrial  stations  reqiiir«stiMmea«rei»«tjf 
an  interval  of  time,  which  even  under  ti»  most  lavoreble 

cases  can  be  only  a  fraction  of  a  tiMWaandtii  of  *««^- 
MetiiodB  of  doing  it,  however,  have  been  deri*>d  and  ex- 
ecuted by  the  l«ibh  physidste,  IW.  Boiic^'««2«* 
Oa«o,  La  quite  «p«itiy  by  Bm^  Ihmmmm^^ 
U.  B.  Naval  Academy,  ^^nnapoiiB.    EK»m  tbei^^Mnipw 


I'ivMi&jmui'mimmm- 


aOLAR  PARALLAX. 


tM  and  tlie  (nm  at  the 
These  qoantities  are 
lifle  measiiremeiit ;  it 
meaavres  of  parallax 
certainty  of  ^  of  its 
the  aim  thb  oorre- 
ilf  a  million  of  miloa. 
or  other  methoda  of 
though  aome  of  theae 
inreaof  parallax,  there 
gun  can  be  detemiined 
racy  which  oharaoter- 

Bdlar  ParallaK.— A 
tnoat  accurate  method 
y  naing  light  aa  a  mea- 
1.    We  ahall  hereafter 
it  the  time  required  for 
rth  is  known  with  oon- 
arly  498  aeoonda.    If 
lily  how  many  miles  or 
,  we  ahall  at  once  have 
^ring  that  quantity  by 
>ont  800,000  IdlomelnM 
■eaeh  about  dght  times 
able  that  two  ])ointa  on 
ndred  Idlometrea  apart 
itinet  Tiaitm  at  dJatanoes 
rare.    Hence  to  deter- 
tdred  for  lig^t  to  pass 
dnM  the  meanmmeat  of 
Oder  the  most  lavonble 
bonaandth  of  a  aeeoad. 
re  been  deyiaed  and  ex- 
FuKAO.  Eoe«A«uri  and 
rign  Mjoikmm  a*  |be 

f^KNB  tha^iia^pMtaiiMi 


■tti 


of  the  bitter,  which  are  probably  the  moit  aoonrate,  the 
velocity  of  light  would  seem  to  be  about  299,900  kilome- 
tres  per  second.  Multiplying  this  by  498,  we  obtain  149,- 
850,000  kilometrea  for  Uie  distance  of  the  sun.  The  time 
required  for  light  to  paw  from  the  sun  to  the  earth  is  still 
uncertain  by  nearly  a  second,  but  this  value  of  the  sun's 
distance  is  probably  the  best  yet  obtained.  The  corre- 
sponding value  of  the  sun's  panllax  is  8**81. 

Yet  other  methods  of  determining  the  sun's  distance 
are  given  by  the  theory  of  gravitation.  The  best  known 
of  these  depends  upon  the  detennination  uf  the  paiallaotio 
inequality  of  the  moon.  It  is  found  by  mathematical  in- 
vestigation that  the  motion  of  the  moon  is  subjected  to 
several  inequalities,  having  the  sun's  horiaontal  parallax 
as  a  iaetiMr.  In  oonseqnenfw  of  the  laigeat «(  these  in- 
eqnaUtiea,  the  motm  ia  about  two  minutea  beliiiid  ita  mean 
phMe  near  the  lint  qnartor,  and  aa  far  in  advance  at  the 
last  quarter.  If  ^  position  of  the  moon  eoidd  be  deter- 
mined hgr  obaervstioa  with-the  same  eiaetaesa  that  the  po- 
siti(«  of  a  alar  or  planet  eaa,  tUa  would  probably  afford 
the  BMBt  aoenrate  method  of  diAerjdniiif  the  adar  par- 
allax. Bnt  aa  obaervatkm  <tf  the  moon  haa  to  be  made, 
not  upon  ita  centre,  but  upon  ita  Bmb  w  etreumfuMice. 
Only  the  limb  neareat  the  sun  ia  viaible,  the  other  one 
bei^g;  uniUuminated,  and  thua  the  illuminated  limb  on 
whieh  the  obaervation  iato  be  made  is  difEerent  at  the  first 
and  third  quarter.  Theae  oonditiona  induee  an  uncertain- 
ty in  <1k.  eomparisim  of  obaerrationa  made  at  the  two 
qnaitara  whieh  cannot  be  entiraly  overomne,  and  therefne 
leave  a  doubt  n^eeting  the  oemetnaai  of  the  reanh. 

Itekf  gjategr  ef  PatarinlnatlnnB  of  the  WtHmt  garallaK. 
— Ae  diafeaaoe  of  tiie  aon  muat  at  all  timet  have  been  one 
of  tiie  BMMt  iBteresting  aekntifieprdblona  prnented  to  the 
human  mfaid.  The  £at  known  attempt  to  effeot  a  adn- 
tioB^f-^  problem  waa  made  by  AmarAiiicnnn,  who  flour- 
iihfilii  ^  thbd  eentwy  before  Obbir.  It  waa  founded 
oftiivfiiMiple  that  the  time  of  the  moon*a  fiiat  quarter 


<vai 


224 


ASTRONOMT. 


will  vary  with  the  ratio  between  the  distance  of  the  moon 
and  Bun,  which  may  be  shown  as  follows.  In  Fig.  ii 
let  JS*  represent  the  earth,  M  the  moon,  and  S  the  sun. 
Since  the  sun  always  illuminates  one  half  of  the  lunar 
globe,  it  is  evident  that  when  one  half  of  the  moon's  disk 
appears  illuminated,  the  triangle  iT  if  ^S  must  be  right- 
angled  at  M.  The  angle  M  E  S  cxa.  be  detennined  by 
measurement,  being  equal  to  the  angular  distance  between 
the  sun  and  the  moon.  Having-  two  of  the  angles,  the 
third  can  be  determined,  because  the  sum  of  the  three 
must  make  two  right  angles.  Thence  we  shall  have  the 
ratio  between  EM,  the  distance  of  the  moon,  and  ES, 
the  distauoe  of  ihe  sun,  by  a  trigonometrical  computation. 


1^ 


Fie.  TO. 


Then  knowing  the  distance  of  the  moon,  which  can  be 
detennined  with  comparative  ease,  we  have  the  distance  of 
the  sun  by  multiplying  by  this  ratio.  Awbtarohcs  con- 
eluded,  from  his  suppMed  measures,  that  the  angle  M  ES 
was  three  degrees  less  than  a  right  angle.    We  should 

then  IwveJ^  =  sin  3"  =  ^  very   nearly.      It  would 

follow  from  this  that  ihe  sun  was  19  times  the  distance 
of  the  moon.  We  now  know  that  this  jwsult  is  entirely 
wrong,  and  that  it  is  impossible  to  determine  the  time 
when  the  moon  is  exactly  half  illuminated  with  any  ap- 
proach to  the  accuracy  necessary  in  the  solution  of  the 
problem.    In  fact,  the  greatest  angular  distuioe  of  the 


i^Wiaft»fe<.W»iMStHWSBIfe.W|!aM8^ 


Iwtance  of  the  moon 
'ollowB.  In  Fig.  ifr" 
oon,  and  S  tho  sun. 
e  half  of  the  lunar 
if  of  the  moon's  disk 
M  S  muBt  he  riglit- 
1  he  detennined  hy 
liar  distance  bet\<reen 
J  of  the  angles,  the 
16  stun  of  the  three 
dce  we  shall  have  the 
the  moon,  and  £S, 
aetrical  computation. 


moon,  which  can  lie 
B  have  the  distance  of 
).  AmsTAROHVs  con- 
that  the  angle  JlfiS'.^ 
t  angle.    We  should 

r   neaiiy.      It  wonld 

19  tunes  the  distance 
this  result  isentarely 
}  determine  the  time 
tminated  with  anjr  ap- 
X  the  solution  of  the 
pAai  distaaee  of  t)ie 


SOLAR  PARALLAX. 


226 


earth  and  moon,  as  seen  from  the  snn — that  is,  the  angle 
E8M — is  only  abont  one  quarter  the  angular  diameter  of 
the  moon  as  seen  from  the  earth. 

The  second  attempt  to  determine  the  distance  of  the 
snn  is  mentioned  by  Ptolemy,  though  Hippabchds  may  be 
the  real  inventor  of  it.  It  is  founded  on  a  somewhat  com- 
plex geometrical  construction  of  a  total  eclipse  of  the 
moon.  It  is  only  necessary  to  state  the  result,  which 
was,  that  the  sun  was  situated  at  the  distance  of  1210  radii 
of  the  earth.  This  result,  like  the  former,  was  due  only 
to  errors  of  observation.  So  far  as  all  the  methods  known 
at  the  time  could  show,  the  real  distance  of  the  sun  ap- 
peared to  be  infinite,  nevertheless  Ptolemy's  result  was 
received  without  question  for  fourteen  centuries. 

When  the  telescope  was  invented,  and  more  aocnrate 
observations  became  possible,  it  was  found  that  the  sun's 
distance  must  be  greater  and  its  parallax  smaller  than 
Ptolkmy  had  supposed,  but  it  was  still  impossible  to  give 
any  measure  of  the  parallax.  AH  that  could  be  said  was 
that  it  was  less  than  the  smallest  quantity  that  could  be  de- 
cided <ni  by  measurement.  The  first  approximaticm  to  the 
true  value  was  made  by  Hokbox  of  England,  and  after- 
ward by  HuYOHKNs  of  Holland.  It  was  not  founded  on 
any  attempt  to  measure  the  parallax  directly,  but  on  an 
estimate  of  the  probable  magnitude  of  the  earth  on  the 
scale  of  the  solar  system.  The  magnitude  of  the  planets 
on  this  scale  being  known  by  measurament  of  their  appar- 
ent angular  diameten  as  seen  frmn  the  earth,  the  solar 
paralkx  may  be  found  when  we  know  the  ratio  between 
the  diameter  of  the  earth  and  that  of  any  planet  whose 
angular  diameter  has  been  measured.  Now,  it  was  sup- 
posed by  the  two  astronomers  we  have  mentioned  that 
the  earth  was  probaUy  of  the  same  order  of  magnitude 
with  the  other  planets. 

HojBBox  had  a  theory,  which  we  now  know  to  be  erro- 
neous iAak  tiie  diameters  of  tiie  pbn^  were  proportional 
to  tita^  distMioes  from  the  Hun—in  other  words,  that  all 


"""Mm 


tl6 


ABTBONOMT. 


tlie  planetR  would  appear  of  the  same  diameter  when  seen 
from  the  stin.  This  diameter  he  estimated  at  28',  from 
which  it  followed  that  the  solar  parallax  was  14".  Ucyobkns 
aisamed  that  the  actual  magnitude  of  the  earth  was  mid- 
way between  those  of  the  two  planets  Ventu  and  Jian  on 
each  side  of  it ;  he  thus  obtained  a  result  remarkably  near 
the  truth.  It  is  true  that  in  reality  the  earth  is  a  little 
kuger  than  either  Ventu  or  MarSf  bat  the  imperfect  tel- 
escopes of  that  time  showed  the  planets  Uu^r  than  they 
really  were,  so  that  the  mean  diameter  of  the  enhufged 
planets,  as  seen  in  the  telescope  of  HmroHrars,  was  such  as 
to  correspond  very  nearly  to  the  diameter  of  the  earth. 

The  first  really  successful  measure  of  the  parallax 
of  a  planet  was  made  upon  Man  during  the  opposition  of 
1672,  by  the  first  of  the  two  methods  already  described. 
An  expedition  was  sent  to  the  colony  of  Oayenne  to  ob- 
serve die  dedinatioii  of  the  planet  from  nig^t  to  night, 
while  corresponding  observations  were  made  at  the  Paris 
Observatory.  From  a  discussion  of  thesi  observations, 
OAsson  obtained  a  solar  parallax  of  9' '5,  wuicih  is  within 
a  second  of  the  truth.  The  next  steps  forward  were  made 
by  the  transits  of  Vmtns  in  1761  and  1769.  The  leading 
dviUied  nations  caused  observadons  on  these  transits  to  be 
made  at  various  pmnts  on  die  globe.  The  method  used 
was  very  simple,  ocmsiBting  in  the  determinati<m  of  the 
timM  at  which  Vmut  entered  upon  the  son's  disk  and  left 
it  again.  The  absolute  times  of  ingress  iad  egress,  as  wen 
from  different  points  of  die  gioto,  might  differ  bjr  90 
minutes  or  more  on  acoonnt  of  panUax.  Tlw  reMha, 
however,  were  found  to  be  diso»d«nt.  It  was  not  imdl 
more  than  half  a  century  had  elapsed:  diat  the  obsemliiE^ 
were  all  carefully  calculated  by  ^okb  of  Germinyy  who 
concluded  that  the  paraUax  of  the  sun  was  8''  8ft7,  aad  the 
distance  95  millions  of  miles. 

In  1854  it  began  to  be  onspeeted  duit  Eirea't  vaihie  of 
die  paraUax  was  m«^  too  small,  and  gMak  labor  imnnF 
devoted  to  a  solndon  of  die  jwoUem.    Hi 


MA88B8  OF  TBB  SUN  AND  EARTH. 


8S7 


I  diameter  when  seen 
bimated  at  28*.  from 
xwasU'.  HcYOHraa 
E  the  earth  was  mid- 
t  Veniu  ttad  Mara  m 
MTult  remarkably  near 
the  earth  is  a  little 
mt  the  imperfect  tel- 
leta  lu-ger  than  they 
leter  of  the  enlarged 

[UTOBBNB,  was  BUOh  88 

meter  of  the  earth, 
imire  of  the   parallax 
Ufing  the  opposition  of 
[)ds  already  deeoribed. 
ly  of  Cayenne  to  ob- 
from  ni^t  to  nij^t, 
ere  made  at  the  Paris 
of  theei  obserratioos, 
!  9'-5,wiuoh  is  within 
eps  forward  were  made 
ndl76».    The  leading 
B  on  these  transitB  to  be 
w.    The  method  used 
B  determination  of  the 
1  the  sui's  disk  and  toft 
nwsimd  egress  88  seen 
«,  mi^t  differ  hj  90 
pmOax.    The  nsiiHa, 
rd^ni.    It  was  not  until 
led!  thai  the  observtliiins 
HOKB  of  Germany,  who 
8nnwaB8'.867,aBdthe 

d  that  "Bxam^M  "nSm  of 

Md  giwt  yborymmf 

em.    Hi        " 


parallaotio  inequality  of  the  moon,  first  fonnd  the  parallax 
oi  the  Sim  to  be  8' -07,  a  quantity  which  he  afterward  re- 
duced to  8". 016.  This  result  seemed  to  be  confirmed  by 
other  observations,  especially  those  of  Mara  during  the 
opposition  of  1862.  It  W8S  therefore  concluded  that  the 
sun's  parallax  was  probably  between  8' '90  and  9^-00. 
Subsequent  researches  have,  however,  been  diminishing 
tliis  value.  In  1867,  from  a  discussion  on  all  the  data 
which  were  considered  of  value,  it  was  concluded  by  one 
of  the  writers  that  the  most  probable  parallax  was  8' '848. 
The  measures  of  the  velocity  of  light  made  by  Miohblson 
iu  1878  reduce  this  value  to  8' '81,  and  it  is  now  doubtful 
whether  the  true  value  is  any  larger  than  this. 

The  obeervati<»s  o^the  transit  of  Vmut  in  1874  have 
not  been  completely  discussed  at  the  time  of  writing  these 
pages.  When  this  is  done  some  further  light  may  be 
thrown  upon  the  question.  It  is,  however,  to  the  deter- 
mination of  the  velocity  of  light  that  we  are  to  look  for 
the  best  result.  AH  we  can  say  at  present  is  that  the  so- 
lar pandhuc  is  probably  between  8' •79  and  8" -88,  or,  if 
outside  these  limits,  tluit  it  can  be  very  little  outside. 


Ol*  THS  SUIT  AVD 


8  8.   XKJLTZVa 


In  sstfmatiiw  oetoitUl  naMS  at  w«U  ss  dIslsBOM,  it  k  I 
to  ttss  t^at  we  may  can  csksrisluaiti^  that  is,  to  tsks  the  bism  <rf 
aaedfBStialboilfasaaait,  iastMdof  saynoUiplsof  tbspoaad 
kaofCBB.     Ite  MMOB  of  tMs  is  that  the  Ados  wmmm  the 


«f  the  phHMlafy  ifstMai.  or,whleh  is  the  mim  thbg,  the 
t  aaeh  be^te  tanas  oftiiat  of  Mne  oae  body  as  the  valt, 


eaabe(btenniae&  ind^pMideatly  of  th«m«Mof  any  one  MT  thcv. 
'AteanveH  a  BMHs  in  Idtognne  or  othor  tanestrial  vmts,  it  is  Beesa* 
■aiTtoiad  liM  aMMof  the  eerth in  endi  anils,  as  already  ex^aiaad. 
TUi,hew«*«t,  isnotaeoMWfylersetwmositeaipnipcys,  wkmnmiij 
Um  rriJattw  msMW  of  the  sevwal  iilsneti  ere  remnitea.  Ineetiaiat* 
iiBtf  tt»  SMHMs  of  QMinffividiHa  ptaaels,  tiiat  of  Ihe  eim  Is  geaefslN 
tdlsnaaannit    The  planetary  nuMee  v^  titen  all  be  very  mbsU 


or  fk«  avCh  mA  Sui^We  Shan  int 
^     >«arthbeQsweitis«0MMcf;8d  hf 
iM|wnJBas  «f  the  an.  Eagn^Hmh 


we  earn 


jjgSf^ggi^mm^BmmmuMmifmmmmfsimimmi 


ns 


AaTUONOMY. 


»!.«  mu.  of  the  mn  relatlre  to  the  euth,  which  is  the  iMiie  thing 
'i^£S,^rAilZlSZm\c^\  m-  o'tb*  •^^h,  th.t  of  the  .«n 
hllnff  unity.  Thl«  m«y  be  dearly  wen  by  reflectin«  th»t  when  we 
knol  the  Sdliw  of  the  ewth'i  orbit  we  can  detennjne  how  fw  the 
ilSh  movJr wSe  from  a  .tndght  line  in  one  wcond  in  connequence 

force  of  the  ran  at  the  dItUnce  of  the  earth.  Comparing  it  with 
the  attractive  force  of  the  earth,  and  making  »"ow«>ce  for  the 
dlieSn^of  dUtancea  from  centres  of  the  two  bodie.,  we  deter- 
mine  the  ratio  between  their  inaMos.  .i„„u  .n<i  •!•. 

The  calculation  in  oueetion  la  made  in  the  mo.t  •imple  and  ele- 
mentarr  manner  as  follows.     Let  us  put : 

ir,  tS  ratio  of  the  circumference  ol  a  circle  to  its  diameter  (ir  = 

"■"151  mL  radius  of  the  earth,  or  the  radius  of  a  sphere  baring 
thd  same  volume  as  the  earth. 

a.  the  mean  distance  of  the  earth  from  the  sun. 

«  the  force  of  Krarity  on  the  earth's  rarface  at  a  point  where  the 
„&i  i.T.ttait*S;  the  distMice  which  a  body  will  fall  in  one 

"*  o*,  the  sun's  attractive  force  at  the  distance  a. 
y.  the  number  of  seconds  in  a  sidereal  year. 
.¥,  the  mass  of  the  sun. 
m,  ttie  uinsa  of  the  earth. 

ktt^ZY^yl^'^T^-^^^J  be  considered  a.  equ^  to 
JSjatffiW^  of  't&'eart^,  or  »» the  -taUnj^W^ 
Ihe  earth  falls  towarTthe  sun  in  one  second  Bj  the  formula  for 
centrifufal  fowe  given  in  Chapter  VIII.,  p.  »04,  we  have, 


■nd  by  the  law  of  gravitation, 


vriienM 


and 


M      4«*o 
„     4ir»a' 


We  have,  in  the  same  way,  for  the  earth, 

m 

whenee 


MASS  OF  THK  BUN. 


lich  U  th«  Mine  thing 
e»rth,  that  of  the  sun 
sflecting  thkt  when  we 
dntf  nnlne  how  fur  the 
!  second  in  conaequenee 
seMuret  the  attrMtive 
h.  Comparing  it  with 
ling  Allowance  for  the 
two  bodies,  we  deter- 

9  moat  timple  and  ele- 

:le  to  its  diameter  (ir  = 

liuB  of  a  sphere  haring 

e  sun. 

kce  at  a  point  where  the 
body  will  fall  in  one 

cea. 
•r. 


be  considered  aa  equal  to 
or  to  the  distance  which 
nd.  By  the  formula  for 
S04,  we  have, 


Thenifore,  ft>r  the  ratio  of  the 


4.r' 


of  the  earth  and  sun,  we  liave : 


4»« 


«  ~  (?  I"    r' 
By  the  formula  for  parallax  In  Ohapter  I.,  |  8,  we  hare: 

1 


r  =  (*8lni'.*.  — .= 


Therefore 


4»' 
ft 


r 
1 


1 


sln«  P 


(»). 


The  (luantities  T,  rand  fl  may  be  regarded  as  all  known  with  great 
eiaotness.  We  see  that  the  mass  of  the  earth,  that  of  the  aun  being 
unity,  is  proportional  to  the  cube  of  the  solar  parallax. 

Prom  d»U  already  giren,  we  hate: 

T^  8M  days,  «  hours,  »"  »*;  In  seconds,  r=  81  688  14», 
Mean  radius  of  the  earth  in  metres,*  .  .  r  =  0  870  008, 
Force  of  grarity  in  metres,    .         .    .    .g—  ■•8X0», 

while  log  w'  =  1  •  59686.    SubetUutIng  these  numbers  in  the  formulw, 
it  may  be  put  in  the  form, 

!lz=[7-88W41sin"P,t 

Jm 

where  the  quantity  in  brackete  is  the  logarithm  of  the  factor. 

It  will  be  codrenient  to  make  two  ohanges  in  the  Miallax  P.  This 
angU  ia  so  exceedingly  small  that  we  may  r«prd  it  as  Mual  to  He 
2^7  To  express  it  In  wtcaai*  wa  must  midttply  it  br  the  number 
clMoonds  in  the  unit  radiua-that  is,  by  «0«»«5".  iWa  will  make 
P  (in  seconds)  =  806865'  sin  P.  Again,  the  standard  to  which  par- 
alkxea  are  re/errwl  is  alwaya  the  earth's  equatorial  radiua,  which  to 
oraatar  than  r  by  about  x\n  of  ito  whole  amount.  So,  if  we  pat /^ 
for  the  «f«a(«rM  hortoontal  paiaUu,  expreaaed  in  aeoMda,  we  shaU 
bave^ 

p' « (1  4-  ill)  806866' ahiP=  18. 81488J  ahiP, 

whence,  for  sin  P  in  terms  of  P*, 
■inP' 

•  tliemeanradlntof  the  earth  to  not  the  «««  of  tito  Po>f  u£ 
equatorial  iwlU.  but  oae  tUrd  the  ram  of  the  polar  n^nAV^ 
ttw  enwtoiial  om,  beeause  we  can  draw  three  such  radii,  each  mak- 
inc«r|ghtaBdt  with  tin  other  twa  ^     ^    ....u. 

^  A  wmbwenclo^d  ta  byMfcati  to^fcwwitty  need  to rfgriiy  tlie 


980 


ABTRONOMT. 


If  we  Bubatitute  this  T»lue  in  the  expreBaion  for  the  quotient  of 
the  masses,  it  may  be  put  into  either  of  the  forms : 


M  _  [6-85498] 


m 


»\4 


P- =[2-78498]  (^j 


The  first  formula  gives  the  ratio  of  the  masses  when  the  solar  pM- 
allax  is  known ;  the  second,  the  parallax  when  the  ratio  of  the  mMSM 
is  known.  The  following  Ubfe  shows,  for  different  values  of  the 
solar  paimllax,  the  corresponding  ratio  of  the  masses,  and  distence  of 
the  sun  in  terrestrial  measures : 


M 
m 

DlMAMOS  or  TBM  BVK. 

Solar 

In  equatorial 

ladUor  the 

earth. 

In  miUioDS  or 
mOee. 

In  miiUoM  of 
kikmietna. 

8' -76 
8' -76 
8* -77 
8" -78 
8'-79 
8*. 80 
8' -81 
8' -86 
8'-88 
8' -84 
8' -86 

887992 
886885 
885684 
884588 
888896 
886968 
881186 
880007 
868867 
867778 
866664 

88578 
23546 
28519 
28486 
88466 
68469 
28418 
68886 
88860 
80888 
68807 

98-421 
98-814 
98-206 
98-108 
96-996 
96-890 
96-788 
96-680 
66-675 
96-470 
96-866 

160-848 
160178 
150001 
148-880 
l«>-660 
148-400 
148-860 
148-161 
148-966 
148-814 
148-646 

We  have  said  thattfae  aoiar  pamlla:  b  wohdrtTeontafaied  betwewi 
theifanits  8".79  and  8'.88.  It  is  oertrinly  baidW  wm  than  on*  or 
twohandndttMoCaseooiidwithoatthem.  So,if  wewlah  to«Mf«M 
the  oonstantsv^ting  tothe  sonin  roond  rnimben,  wemayaaytlMt-- 

»■  iiMW  is  880,000  times  flwi  of  the  earth. 

It.  i««i«»  In  miles  is  96  milHoofc  «r  pfb^p*  »  H^  hM. 

Jti  distance  in  kfloawtrss  is  pwWily  betwem  149  and  160  mil- 

liens.  ji 

IlMiat^  ^  tlw  ton.— A  temaikable  res^  of  the  pnoedlug 
inveatioaikmisthat  the  denrf^  of  the  taa,  witaHve  to  tt^  <rf  ttie 
e^STSnbe  detnmined  indep^ently  of  the  ma*  or  distence  of 
the  san  by  measuriag  its  appwent  aoguUr  diaawter,  and  the  fowe 
of  gimvity  at  the  earth's  surface.  I«t  us  pot 
.^,  the  deiu%  of  Um  son. 


nH^^S; 


n  for  the  quotient  of 


ms; 


M  when  the  solar  pur- 
he  ratio  of  the  mMses 
lifferent  values  of  the 
asses,  and  distance  of 


>r  TBM  BVH. 


lODSOf 

In  milUoM  of 

M. 

kikNmtm. 

m 

lSO-848 

114 

1S0178 

906 

180001 

102 

148-880 

B96 

l«>-800 

BW 

148-480 

786 

148-880 

880 

148- in 

S7S 

148-988 

410 

148-814 

888 

148-648 

Mt  contained  between 
ardlT  more  than  on«  or 
>,  if  we  wish  to  onreaa 
ben,  wemajaayftal^ 

MaHttielats. 

reen  148  and  160  mil- 

MoH  of  the  preoedliq; 
leitatiTe  to  tiSat  «rf  tin 
iM  nuM  or  distance  of 
Uattflter,  and  the  fone 

t  ■ 


JramtfMMVtti.  Hmmi, 
U 


MASS  OF  THE  -8K2V. 


S81 


Linear  radius  of  the  sun  =  a  sin*. 
Tolume  of  the  sun 


4^   ,  .  , 
=  —  o'  sin*  • 
8 


(froui  the  formula  for  the  volume  of  a  sphere). 


4ir 


Mass  of  the  sun,    Jf  =  -  3  «'  ■»  b»«>'  »• 

4ir 
Mass  of  the  earth,  m=-^r  a. 

Substituting  these  values  of  M  and  m  in  the  equation  (a),  and 
dividing  out  &e  common  factors,  it  will  become 

D  .  4irV 

J  sin  •=  yiy* 

from  which  we  find,  for  the  ratio  of  the  density  of  the  earth  to  that 
ofthesun,  ^  . 

This  eouation  solves  the  probten.  But  the  wlution  may  be  trana- 
f«™idt2?™«irion  We\now  from  the  Uw  of  falUng  bodies  that 
?Wvv  bX^rin  the  time  «,  fall  through  the  distance  4 «r/. 
H^TheffitoTiVi.  double  tile  distance  which  a  bod,  wouli  faU 
•  ^a«1j^  if  flie force <rf  aniTity could  act  upon  it oontinu- 

^wffl  be  the  number  of  radU  of  the  earth  through  which  the 
b!d/  will  fall  in  a  sidereal  year.  If  we  put  F  for  this  number,  the 
proeeding  equation  will  become, 


We  therefoce  have  thia  rak  fbr  finding  the  denaity  of  the  earth 
'^  jSj?:tJi^'^' «•  «ra  a  Aesey  fe.^  .P^ 

■  "y. *°^  rTFlr^zJ^.^*!^  4Sm»»«f  aMmitina  «a«  «»<»'•  stir- 

riom  the  namerieal  data  alrei^y  given,  we  find : 
DoMity  of  earth,  that  of  ran  being  unity. 


i 
5' 


>8-8Me. 


232 


A8TR0N0MT. 


Density  of  the  aun,  that  of  tho  eurth  being  unity, 
?  =  025606. 

Them  relations  do  not  give  us  the  actual  density  of  either  body. 
We  have  said  that  Uie  mean  density  of  the  earth  is  about  6t,  that  of 
water  being  unity.  The  sun  is  therefore  about  40  or  60  per  cent 
denser  than  water. 

Mtt—oa  of  the  Flanete.— If  we  knew  how  far  a  body  would 
fall  in  one  second  at  the  surface  of  any  other  planet  than  the  earth, 
we  could  determine  its  mass  in  much  the  same  way  as  we  have  de- 
termined that  of  the  earth.  Now  if  the  planet  has  a  satellite  re- 
volving around  it,  we  can  make  this  detennination — not  indeed 
directly  on  the  surface  of  the  planet,  but  at  the  distance  of  the  sat- 
ellite, which  will  et^ually  give  us  the  required  datum.  Indeed  by 
observing  the  periodic  time  of  a  satellite,  and  the  angle  subtended  by 
the  major  axis  of  its  orbit  airound  the  planet,  we  have  a  more  direct 
datum  for  determining  the  mass  of  the  planet  than  we  actually  have 
for  determining  that  of  the  earth.  (Of  course  we  here  refer  to  the 
masses  of  the  planets  relative  to  that  of  the  sun  as  unity.)  In  fact 
could  an  astronomer  only  station  himself  on  the  planet  Vemu  and 
make  a  series  of  observations  of  the  angular  distance  of  the  moon 
from  the  earth,  he  could  determine  the  mass  of  tho  earth,  and 
thence  the  solai  parallax,  with  far  greater  precis'o"  than  we  arc  like- 
ly to  know  it  for  centuries  to  come.  liet  ui  u^<  a-XQOaider  the 
equation  for  M  found  on  page  288  : 


Jf=f 


4ir»a' 


Here  a  and  7*  may  mean  the  mean  distance  and  periodic  time  of 

Or* 

any  planet,  the  quotient  -^  being  a  constant  by  Ebtucb's  third 

law.  In  the  same  equation  we  may  suppose  a  the  mean  distanoe  of 
a  satellite  from  its  primarv,  and  T  its  time  of  revohition,  and  JTwill 
then  represent  the  maas  of  the  planet.  We  shall  have  timefme  for 
the  mass  of  the  planet, 

4ir««« 


a'  bdng  the  mean  distance  of  the  satellite  from  'the  planet,  and  t' 
its  tinw  of  revolution.  Therefore,  for  the  masa  of  the  phHMt  lel 
ative  to  that  of  the  sun  we  have  : 

m      of  T* 


Let  na  Mnmoae  a  to  be  the  mean  diataaoe  <rf  the  phnefe  fran  the 
son,  in.wUeh  eeae  Tmuat  lepreaent  its  time  of  nmdatioii.  Tbnm, 
if  we  put  •  fw  the  angle  subtended  hythemdhM  of  tiie  oiMt  of  the 


MA88B8  OF  TUR  PLANKTB. 


383 


nity, 


nsity  of  either  body. 
1  IB  about  Sf,  that  of 
ut  40  or  60  per  cent 

w  far  a  body  would 
lanet  than  the  earth, 
way  as  we  have  de- 
let  has  a  satellite  re- 
linaAion — not  indeed 
e  distance  of  the  sat- 
l  datum.  Indeed  by 
lie  angle  subtended  by 
re  have  a  more  direct 
;han  we  actually  have 

I  we  here  refer  to  the 
a  as  unity.)  In  fact 
he  planet  Venxu  and 
listance  of  the  moon 
Bs  of  the  earth,  and 
is'n"  than  we  arc  like- 

II  m"    )  consider  the 


tnd  periodic  time  of 

\  by  KBn.BB's  third 

)  the  mean  distance  of 
reTolntion,  and  JTwill 
laU  have  therefore  for 


imthe  planet,  and  T' 
taw  of  the  ptauwt  rel 


\  the  pianet  from  ths 

of  NVtHOtlOll.     ^MBf 

ihM  Of  th9  oiliik  of  ttiB 


satellite,  as  seen  from  the  sun,  we  shall  have,  assuming  the  orbit 
to  be  seen  edgewise, 


8in<  =  — 
a 


If  the  orbit  is  seen  in  a  direction  perpendicular  to  its  plane,  we 
should  have  to  put  tang  <  for  sin  « in  this  formula,  but  the  angle 
B  is  80  small  that  the  sine  and  tangent  are  almost  the  same.  If  we 
put  T  for  the  ratio  of  the  time  of  revolution  of  the  phuiet  to  that  of 
the  satellite,  it  will  be  equivalent  to  supposing 


T 

The  equation  for  the  mass  of  the  planet  will  then  become 

5:=r*8ln«., 

which  is  the  simplest  form  of  the  usual  formula  for  deducing  the 
mass  of  a  phinet  from  the  motion  of  its  satellite.  It  in  true  that  we 
cannot  observe  •  directly,  since  we  cannot  place  ourselves  on  the 
sun,  but  if  we  observe  the  angle  a  from  the  earth  we  cm  always 
reduce  it  to  the  sun,  because  we  know  the  nroportion  between  the 
distances  of  the  pUnet  from  the  earth  ud  frmn  the  sun. 

All  the  Uu^  planets  outside  the  earth  have  satellites ;  we  can 
therefore  determine  their  masses  in  this  simple  way.  The  earth 
having  also  a  satellite,  its  mass  could  be  determined  in  the  smm 
way  but  for  the  ofarcumstance  ahteady  mentioned  that  we  capnot 
determine  the  distance  of  the  moon  ip  planetary  units,  as  we  (wi 
the  distance  of  the  satellites  of  the  othor  planeU  from  their  pri- 
maries. 

file  phwets  Mtnwry  and  Vanut  have  no  satellites.  It  is  therefore 
necessary  to  determine  their  masses  by  thdr  influence  in  altering 
the  elliptic  motions  of  the  other  planets  rmmd  the  son.  The  altera' 
tions  thus  prodnoed  are  for  the  most  part  so  small  that  thefar  deter- 
mination is  a  practical  problem  of  some  difBiml^.  Thusthe  action 
of  JftrwMrw  on  tiie  neighboring  planet  Vmu»  rarefy  changes  the  po- 
dtion  of  the  hitter  \if  more  than  one  or  two  seconds  <4  are,  mileae 
we  eompare  observatimu  more  than  a  cmtnry  apart  But  regular 
and  accurate  obaervatlmis  of  Ymim  were  rarely  made  until  after  tlM 
beginning  of  this  oentary.  The  mass  of  Vmtu  is  best  detemhMM 
by^idliience  of  tke  plaaet  fa  dmaging  the  porition  of  the  pine 
of  the  euib*s  orbit.  Altogellwr,  the  determination  of  the  bmssm 
of  Jbmcrw  and  Vmtm  preseata  one  of  the  most  complicated  |^rob> 
loDB  with  wUch  the  mathematieal  artrommier  has  to  deal. 


CHAPTER   X. 

THE  REFRACTION  AND  ABERRATION  OF  LIGHT. 
i  1.    ATMOSPHXBIO  BBFBAOTIOH. 

When  we  refer  to  the  place  of  a  planet  or  star,  we 
usually  mean  ita  tnte  place-*.*.,  its  direction  from 
an  obierver  ritnated  at  the  centre  of  the  earth,  consid- 
erad  as  a  geometrical  point.  We  have  ahown  m  the  aeo- 
tion  on  parallax  how  obeervationa  which  Me  nef«anly 
taken  at  the  anrfaoe  of  the  earth  are  reduced  to  what  they 

wonld  have  been  if  the  observer  were  Mtuated  at  toe 
earth's  centra.  In  this,  however,  we  have  auppoeed  the 
Btarto  appear  to  be  projected  on  the  celertial  «phef  "^ 
the  prolS^Ition  of  the  line  joining  Ae  observer  MidAe 
star  TlM  ray  from  the  star  is  considered  as  if  It  Buffered 
no  deflection  in  passing  through  ihe  stellar  spaces^ 
through  the  earth's  atmosphere.  But  from  the  prmc^ 
of  p^ics,  welmow  that  such  a  luminousray pa«ng  from 
^^^tr«P«»  («.  the  rtdlar  qp«»i  are),  and  ihroiyj^ 
.tmo.Jh^™.5afferarohjjd^^ 

is  known  to  do  in  pamng  fewm  a  »««™o  .vST^ 
riH)dium.    As  we  see  the  star  in  the  direction  which  ha 

Hriit  beam  has  when  it  enteia  the  ej^-0»t ».  •■  *«  F»- 
i^  the  star  on  the  celestial  sphere  by  l^^^^J^ 
&t  beam  backwaid  into  space-there  murt  be  ""TO"- 
ent  dispUwement  of  the  star  from  refraction,  and  it  is 

this  which  we  are  to  eoosidw. 

We  may  reoaU  a  few  definitions  from  0iy««».    ^ 
i»y  which  Ujaves  the  itM  and  implngei  on  the  outer  m- 


[ON  OF  LIGHT. 

AOnOH. 

planet  or  star,  we 
s  direction  from 
the  earth,  consid- 
I  shown  in  the  sec- 
ich  are  neoewarily 
inoed  to  what  thej 
ire  sitnated  at  the 
have  sappoBod  the 

celestial  sphere  in 
e  ohaenrer  and  the 
red  M  if  it  infEend 

steDar  spaoea  and 
from  the  prinoipliM 
)iuT»7pMRing  tnm 
re),  and  ihro«|i^  aa 
IB  ever/  my  of  li^i 
rare  into  a  deoMf 
diraetion  whksh  ita 
-that  is,  aa  we  pio- 
by  pn^mging  lliia 
pemnatbeanappar- 
efraetion,  and  it  ia 

bom  phyrioa.    The 
a  on  tii0  oater  m^ 


RBFRAOTION. 


285 


face  of  the  earth*B  atmosphere  is  called  the  inoident  ray  ; 
tdXeir  its  deflection  by  the  atmosphere  it  is  called  the  re- 
fracted ray.  The  difference  between  these  directions  is 
called  the  aatronamical  r^raation.  If  a  normal  is  drawn 
(perpendicnlar)  to  the  surface  of  the  refracting  medium  at 
the  point  where  the  incident  ray  meets  it,  the  acute  angle 
between  the  incident  ray  and  the  normal  is  called  the 
angle  of  incidence,  and  tiie  acute  angle  between  the  nor- 
mal and  the  refracted  ray  is  called  the  angle  of  refraction. 
The  refraction  itself  is  the  difference  of  these  angles. 
The  normal  and  both  incident  and  refracted  rays  are  in 
the  same  vertica]  plane.  In 
Fig.  69  i^^  ia  the  ny  incident 
upon  the  snrfaoe  BA  of  the  re- 
fracting medinm  B'  B  A  Sf,. 
A  C  n  the  refracted  ray,  MJf 
the  normal,  SA  Jf  and  CAN 
the  angles  of  inddoioe  and  i«- 
fraction  respectively.  Prodvoe 
C  A  backward  in  the  direotion 
AST  :  SAJSn»the  refraetion. 
An  observer  at  (7  will  aee  tiie 
star  .$ as  if  it  were  tAST.  AS 
is  the  apparent  direction  of  tiie  ray  from  the  star  8^  and 
S  ia  the  qgparmU  plant  ot  Um  atar  aa  affaeted  by  refrac- 
tion. 

This  suppoaes  the  qiaoe  above  ^  ^  in  tlie  figure  to  be 
entirely  empty  apaoea,  and  the  earth's  atmoaphere,  equally 
denaethroq^ont,tofiUtheapaoebelowJ?J9'.  Intact,  how- 
evw,  the  eaoith'a  atmoaphere  b  moat  denae  at  the  snrfaoe  of 
the  earth,  and  gradually  diminiahea  in  dwiaity  to  ita  exterior 
bonndary.  Therefore,  if  we  wish  to  repreamt  the  facta  aa 
they  are,  we  mnat  auppoae  the  atmoaphere  to  be  divided 
into  a  great  number  of  parallel  layera  of  air,  and  by  as- 
suming an  infinite  number  of  these  we  may  also  assume  that 
throoi^oiit  eaeh  of  tiiem  tiie  air  k  equally  dense.  Hence 
Hie  pieoeding  figum  wiU  only  rcpreaent  the  refraetion  at 


jtStmHmmtmmmmm 


886 


A8TB0N0MT. 


a  sinirle  one  of  these  layere.  It  follows  from  this  that  t  lo 
path  of  a  ray  of  light  through  the  atmosphere  is  not  a 
straight  line  like  A  C,  but  a  curve.  We  may  suppose 
this  curve  to  be  represented  in  Fig.  70,  where  the  num- 
ber of  layers  has  been  taken  very  small  to  avoid  conf  usmg 

the  drawing.  ,  ,  .        ,  . . 

Let  C7  be  the  centre  and  A  a  pomt  of  the  surface  of  the 
earth ;   let  -S"  be  a  star,  and  5  «  a  ray  from  the   star 
which  is  refracted  at  the  various  layers  into  which  we  buj, 
pose  the  atmosphere  to  be  divided,  and  which  finally 


na.  79.— nvBAonoiT  or  t^mB  or  An. 

enters  the  eye  of  an  observer  at  A  in  the  JPP^"*  ^^ 
tion  A  JSr.  He  will  then  see  the  star  m  the  direction  ^ 
instead  of  that  of  S  8,  and  SASTy  the  refraction,  will 
throw  the  star  nearer  to  the  zenith  -Z.  . 

The  angle  i^AZis  Uie  apparent  zenith  distance  of  A  , 
the  true^nith  distance  of  -S  is  Z^  ^,  and  this  imyr  be 
assumed  to  coincide  with  8e,  as  for  all  heavenly  bodies 
except  the  moon  it  practically  does.  The  hne^.  pro- 
longed  will  meet  the  line  ^  Z  in  a  point  above  A,  sup- 
pose at  &'. 


HEFRACTION. 


237 


rs  from  this  that  tlio 
itmosphero  is  not  a 
We  may  suppose 
0,  where  the  num- 
1  to  avoid  confusing 

of  the  surface  of  the 
ray  from  the   star 
B  into  which  we  bui> 
,  and  which  finally 


or  tOL. 
i  the  apparent  direc- 
tar  in  the  direction  S 
',  the  refraction,  will 

T 

'*  '. 

zenith  distance  of  ^; 

A.  Sy  and  this  may  be 
r  all  heavenly  bodies 

B.  The  line  Se  pro- 
point  above  A,  s^p- 


Law  of  Beflraotion. — A  considvration  of  tlio  pliyHicitl  condi- 
tiona  involved  has  Ivd  to  tlio  following  form  for  tliu  rcfrucition  in 
zenith  distance  (A  i), 

(A{)  =  ^tan(f'-aAO), 

in  which  T  i*  the  apparent  zenith  distance  of  the  star,  and  ^  is  a 
constant  to  be  determined  by  observation.  A  is  found  to  be  about 
67',  so  that  we  may  write  (A  0  =  "''"  t***  ^'  approximately. 

Thi<«  expression  gives  what  is  called  the  mean  refraction — that  is, 
the  »<f  raction  corresponding  to  a  mean  state  of  the  barometer  and 
thermometer.  It  is  clear  that  changes  in  the  temperature  and  pres- 
sure will  affect  the  d'  •»<*«  of  'he  air,  and  hence  its  refractive  power. 
The  tables  of  the  mt  *  -  <kCtion  made  by  Besbri.,  based  on  a  more 
accurate  formula  than  >.iie  one  above,  are  now  usually  used,  and  these 
are  accompanied  by  auxiliary  tables  giving  the  small  corrections  for 
the  state  of  thii  meteorolo^cal  instruments. 

Let  us  consider  some  of  the  consequences  of  refraction,  and  for 
our  purpose  we  may  take  the  formula  (A{)s=57'  tan  C,  m  it 
very  nearly  represents  the  facts.  At  T  =  0  (A  ()  =  0,  or  at  the 
apparent  zenith  thnre  is  no  refraction.  This  we  should  have  antici* 
pated  as  the  incident  ray  in  itself  normal  to  the  refracting  surface. 

Tlie  following  extract  from  a  refraction  table  gives  the  amount  of 
refraction  at  various  zenith  distances  : 


ir 

(AC) 

c 

(Af) 

0° 

C        0* 

70» 

8'         89' 

10" 

V       10' 

80° 

5'      ao' 

ao° 

0'       88* 

86° 

W          0" 

45° 

V       08' 

88° 

18'          C 

no* 

r    w 

88° 

84'         8S' 

»• 

1'       40' 

•0° 

84'         80' 

Quantity  and  SflBbota  of  Beflraotion. — At  45°  the  refrac- 
tion is  about  1',  and  at  90°  it  is  34'  30"— that  is,  bodies  at 
the  zenith  distances  of  45°  and  90°  appear  elevated  above 
their  true  places  by  1'  and  841'  respectively.  If  the  sun 
has  just  risen — that  is,  if  its  lower  limb  is  just  in  apparent 
contact  with  the  horizon,  it  is,  in  fact,  entirely  below  ihe 
true  horizon,  for  the  refraction  (SS*)  has  elevated  its  cen- 
tre by  more  than  its  whole  apparent  diameter  (32'). 

The  moon  is  faU  whran  it  is  exactly  opposite  the  son, 
and  tlMwfore  were  thei«  no  atmosphere,  moon-rise  of  a 
ftdl  mbmt  and  simiet  wonld  be  simnltaoeons.    In  &ct, 


atiMllilHiiilili*!**"'^"!!''  ii'W-iMiiiiinawiu 


yaummmf^ 


A8TR0N0MY. 

both  bodiei  being  elevated  by  refraction,  we  see  the  fnll 
moon  risen  before  tlie  sun  has  set.  On  April  aotli,  1887, 
the  full  moon  rose  eclipsed  before  the  snn  had  set. 

We  see  from  the  table  that  the  refraction  varies  com- 
paratively little  between  0°  and  60°  of  zenith  distance,  but 
that  beyond  80°  or  85**  its  variation  is  quite  rapid. 

The  refraction  on  the  two  limbs  of  the  sun  or  moon  will 
then  be  different,  and  of  course  greater  on  the  lower  limb. 
This  will  apparently  be  Ufted  up  toward  the  upper  limb 
more  than  the  upper  limb  is  Ufted  away  from  it,  and 
hence  the  sun  and  moon  appear  oval  in  shape  when  near 
the  horizon.  For  example,  if  the  zenith  distance  of  the 
sun's  lower  limb  is  85°,  that  of  the  upper  will  be  about 
84°  28',  and  the  refractions  from  the  tables  for  these  two 
zenith  distances  differ  by  V  ;  therefore,  the  sun  will  ap- 
pear oval  in  shape,  with  axes  of  82'  and  81'  approxi- 
mately. 

Detarmination  of  Befraotion.— If  we  know  the  law  aeeordiBg 
to  which  refmotioii  varies — ^that  is,  if  we  have  an  accurate  formula 
which  will  give  (  A  C)  in  terms  of  {;  we  can  determine  the  absolute 
reft«ction  for  unr  one  point,  and  from  the  law  deduce  it  for  any 
other  points.  Thus  knowing  the  horizontal  refraction,  or  the  t«- 
fraction  in  the  horiaon,  we  can  determine  the  refraction  at  other 
known  senith  distances. 

We  know  the  time  of  (theoretical  or  true)  sunrise  and  sunset  1^ 
the  fimnute  of  1 7,  p.  44,  and  we  may  observe  the  time  of  apparent 
riring  and  settuig  of  the  sun  (or  a  star).  The  difference  of  these 
times  gives  a  means  of  determining  the  effect  of  refraction. 

Or,  m  the  observations  for  latitude  by  the  method  of  {  8,  p.  47,  we 
can  measure  the  apparent  polar  distanoes  of  a  drcnmpolw  star  at 
its  upper  and  lower  culmination.  Its  polar  distances  above  and 
below  pole  should  be  equal ;  if  there  were  no  refraction  they  would 
be  so,  but  they  really  differ  by  a  quantity  which  it  is  easy  to  see  b 
the  difference  of  the  refractions  at  lower  and  upper  culminations. 
By  chooring  suitable  ciicumpolar  stars  at  various  polar  distances, 
tlus  difference  may  be  determined  for  all  pobur  distwoes,  and  tiiere> 
fore  at  all  senith  distances. 

g  S.    ATWBBATIOW  AXD  THX  WyBtXXS  OF  LKIHS. 

Berides  rafradion,  there  is  another  oanae  whidi  preTents 
our  seeing  the  oekatial  bodies  exaet^  in  the  tnw  direoHoa 
in  which  they  lie  &om  i»— namely,  Ae  progreMve  mo- 


ion,  we  see  the  full 
►n  April  aoth,  1837, 
sun  had  Bot. 
fraction  varies  com- 
'  zenith  distance,  but 
quite  rapid, 
the  sun  or  moon  will 
ir  on  the  lower  limb, 
^ard  the  upper  limb 
I  away  from  it,  and 
in  shape  when  near 
nith  distance  of  the 
upper  will  be  about 
tables  for  these  two 
ore,  the  sun  will  ap- 
12'  and  31'  approxi- 

e  know  the  law  Mcording 
lave  tn  accunte  fonnuta 
a  determine  the  abwlute 
«  law  deduce  it  for  any 
lUl  fefraction,  or  the  n- 
e  the  refraction  at  other 

le)  annrise  andninaetl^ 
ivre  the  time  of  apparmt 
The  difference  of  theee 
Eect  of  refraction, 
le  method  of  1 8,  p.  47,  we 
M  of  a  drcnmpolar  atar  at 
ofaur  distances  above  and 
» no  refraction  they  would 
rwhichHiseaqrtoMeis 
r  and  upper  culminations, 
i  Twrloua  polar  distances, 
polar  ^stances,  and  th«e- 

montoK  ov  uobs. 


sr  cause  wl 

i^  in  the  tme  diraotka 

ly,  the  progroMive  ma- 


ABmsATioir. 


339 


tion  of  light.  We  now  know  that  we  see  objects  only 
by  thu  light  which  emanates  from  them  and  reaches  our 
eyes,  and  we  also  know  that  this  light  reijuirus  time  to 
pass  over  the  space  which  separates  us  from  the  object. 
After  the  ray  of  light  once  leaves  the  object,  the  latter 
may  move  away,  or  even  be  blotted  out  of  existence,  but 
the  ray  of  light  will  continue  on  its  course.  Consequent- 
ly when  we  look  at  a  star,  we  do  not  see  the  star  that  now 
is,  but  the  star  that  was  several  years  ago.  If  it  should  be 
annihilated,  we  should  still  see  it  during  the  yean  which 
would  be  required  for  the  last  ray  of  light  emitted  by  it  to 
reach  us.  The  velocity  of  light  is  so  great  that  in  all  ob- 
servations of  terrestrial  objects,  our  vision  may  be  regarded 
as  instantaneous.  But  in  celestial  observations  the  time 
required  for  the  light  to  reach  us  is  quite  appreciable  and 
measurable. 

The  discovery  of  the  propagation  of  light  is  among  the 
most  remarkable  of  those  made  by  modem  science.  The 
fact  that  light  requires  time-  to  travel  was  first  learned  by 
the  observations  of  the  satelUtes  of  Jupiter.  Owing  to 
the  great  magnitude  of  this  planet,  it  casts  a  much  longer 
and  larger  shadow  than  our  earth  does,  and  its  inner  sat- 
ellite is  therefore  edipeed  at  every  revolution.  These 
eclipses  can  be  observed  from  the  earth,  the  satellite  van- 
ish^ from  view  as  it  enters  the  shadow,  and  suddenly 
reappearing  when  it  leaves  it  again.  The  aoenracy  with 
which  the  times  of  this  disappearance  and  reappearance 
could  be  observed,  and  the  consequent  value  of  «ach  ob- 
serrationB  for  the  detormination  of  longitudes,  led  the 
artronomms  of  the  seventeenth  oentnry  to  make  a  careful 
study  of  the  motions  of  these  bodies.  It  was,  however, 
neoessaiy  to  make  tables  by  which  the  times  of  ^le  eclipan 
could  be  piredi<tfed.  It  was  found  by  Bomont  that  these 
timcn  depended  on  the  dirtanoe  of  Jt/ypHmr  from  the  earUi. 
If  he  made  his  tables  agree  with  obaemitiiMM  when  the 
enth  wae  nearest  tft^pUert  it  was  found  ^t  as  the  earth 
receded  &mn«Aifwlsr  in  ^  aDnnaloonne  around  the  snoi 


TT"? 


'"nmmm, 


MO 


ASTRONOMY. 


tlio  oclipficM  wcro  constantly  seen  later,  until,  wlion  ut  itH 
gruuteHtdiKtance,  tliu  tiniuH  apjiearud  tu  liu  22  niinutiw  latu. 
lioiiifKK  saw  that  it  was  in  the  highesc  degree  improbable 
that  the  actual  motions  of  the  satellites  should  be  affected 
wttli  any  such  inequality  ;  he  therefore  propounded  the 
bold  theory  tliat  it  took  time  for  light  to  come  from  Ju- 
piter  to  the  earth.  The  extreme  differences  in  the  times 
of  the  eclipse  being  22  minutes,  he  assigned  this  as  the  time 
required  for  light  to  cross  the  orbit  of  the  earth,  and  so 
concluded  that  it  came  from  the  sun  to  the  earth  in  1 1 
minutes.  We  now  know  that  this  estimate  was  too  great, 
and  that  the  true  time  for  this  passage  is  about  8  minutes 
and  18  seconds. 

DiMMTcrj  of  Ab«rr»tioii. — At  first  this  theory  of  'Ron- 
iiBR  was  not  fully  accepted  by  his  contemporaries.  But 
in  the  year  1729  the  celebrated  Bbadlbt,  afterward  As- 
tronomer Boyal  of  England,  discovered  a  phenomenon  of 
an  entirely  different  chunoter,  which  confirmed  tlie  theory. 
He  was  then  engaged  in  making  observations  on  the  star 
y  Dro/DOM*  in  order  to  determine  its  parallax.  The  effect 
of  parallax  would  have  been  to  make  the  declination 
greatest  in  June  and  least  in  December,  while  in  Mardi 
and  September  the  star  would  occupy  an  intermediate  or 
mean  position.  But  the  result  was  entirely  different. 
The  declinations  of  Jnne  and  December  were  the  same, 
showing  no  effect  of  parallax  ;  but  instead  of  remaining 
oonstant  the  rest  of  the  year,  tJie  declination  was  some  40 
seconds  greater  in  September  than  in  March,  when  the 
effect  6i  paralha  would  be  the  same.  This  showed  that 
the  direction  of  the  star  appeared  different,  not  aooording 
to  the  position  of  tlie  earth,  but  aooording  to  the  direction 
of  its  motion  around  the  ran,  the  star  being  apparently 
displaced  in  this  direction. 

It  has  been  said  that  the  explanation  of  this  singular 
anomaly  was  fint  snggested  to  Bbaduet  while  sailing  on 
the  Thames.  He  notioed  that  when  his  boat  moved  nq^d- 
ly  at  right  angles  to  the  tme  direction  of  the  wind,  die 


ABMlUtATION. 


U\ 


r,  until,  when  vX  its 
o  tic  22  ininutott  late, 
t  degree  improbable 
»  Bhould  be  affected 
fore  propounded  the 
t  to  come  from  Jtt- 
{erences  in  the  times 
igned  this  as  the  time 
of  the  earth,  and  so 
n  to  the  earth  in  11 
itiraate  waa  too  great, 
«  is  about  8  miirates 

t  this  theory  of  Rok- 
Bontemporariea.  But 
ADLET,  afterward  Aa- 
sred  a  phenomenon  of 
confirmed  the  theory, 
servations  on  the  atar 
,  parallax.  The  effect 
nake  the  declination 
mber,  while  in  Hardi 
py  an  intermediate  or 
as  entirely  different, 
smberwere  the  same, 

instead  of  remaining 
iclination  was  some  40 

in  March,  when  the 
le.  This  showed  that 
ifferent,  not  aMording 
ioiding  to  the  direction 

■tar  being  apparently 

tation  of  this  singular 
iDLCT  while  sailing  on 
p  hit  boat  moved  r«|p$d- 
stion  of  the  wind,  the 


apparent  direction  of  the  wind  changed  toward  the  point 
whither  the  boat  was  going.  When  the  boat  sailed  in  an 
opposite  direction,  the  apparent  direction  of  the  wind  sud< 
denly  changed  in  a  corresponding  way.  Here  was  a  phe- 
nomenon very  analogous  to  that  which  he  had  observed  in 
the  stani,  the  direction  from  which  the  wind  appeared  to 
come  corresponding  to  the  direction  in  which  the  light 
reached  the  eye.  This  direction  changed  with  the  mo- 
tion of  the  observer  according  to  the  same  law  in  the  two 
cases,  fie  now  saw  that  the  apparent  disphuwment  of  the 
star  was  due  to  the  motion  of  the  rays  of  light  combined 
with  that  of  the  earth  in  its  orbit,  the  apparent  direction 
of  the  star  depending,  not  upon  the  absolute  direction 
from  which  the  n,y  comes,  but  upon  the  relation  of  this 
direction  to  the  motion  of  the  observer. 

To  show  how  this  is,  let  J.  j9  be  the  optical  axis  of  a 
telesoope,  and  S  a  star  from  which  emanatea  a  ray  mov- 
ing  in  the  true  direction  S  A  R, 
Perhaps  the  reader  will  have  a  clearer 
oonoeption  of  the  subject  if  he  imi^ 
iuea  ji  J?  to  be  a  rod  which  an  ob* 
server  at  B  w^  to  point  at  the  star 
a.  It  ii  evi4«|it  Hun  he  wiU  pomt  j 
thia  rod  in  wtidk  •  1P|^  that  the  ray 
of  light  sitallifi^^BHWMUJy  along  iti 
length.  SappQ#  iHiw  that  the  ob- 
server Ia  moviiif  Iron  JSu>wud£' 
with  auch  a  vdkMitj  that  he  movw  I 
from  B  Ut  B*  during  the  time  to.  _. 

quired  for  any  of  light  to  move  from  '».  tb. 

AXttS.  Bappoie  alio  that  the  ray  of  light  ^:iiieaehea 
.i  at  the  wme  time  that  the  end  of  his  rod  deea.  Then 
it  is  elear  that  wUk  the  rod  ia  movfaig  from  the  position 
^  .ff  to  the  poaition  utV^,  the  my  of  %ht  win  move  from 
A  to  JS'^ittid  win  tiMiefaranmaoonmtely  along  the  kngth 
of  therod.  ggg  iiwrwim,  if  th  one  tMid  of  the  way 
tram  ir  to  ^,than  tlLe]i|^t,at  theinatantof  tho  rodtak. 


KMMI 


ABTRONOMT. 

ing  the  porition  h  a,  will  be  one  third  of  the  w»y  from  A 
to  B\  and  will  therefore  be  aoourately  on  the  rod.  Con- 
loquently,  to  the  observer,  the  rod  will  appear  to  be  point- 
ed at  the  star.  In  reality,  however,  the  pointing  will  not 
be  in  the  true  direction  of  the  star,  bnt  will  deviate  from 
it  by  an  angle  of  which  the  tangent  is  the  ratio  of  the 
velocity  with  which  the  observer  is  carried  along  to  the 
velocity  of  light.  This  presopposes  tliat  the  motion  of  the 
observer  is  at  right  angles  to  that  of  a  ray  of  light.  If 
this  is  not  his  direction,  we  mast  resolve  his  velocity  into 
two  components,  one  at  right  angles  to  the  ray  and  one 
parallel  to  it.  The  latter  will  not  affect  the  apparent  di- 
rection of  the  star,  which  will  therefore  depend  entirely 
upon  the  former. 

Sflbota  of  Abemtion. — The  apparent  displacement  of 
the  heavenly  bodies  thns  produced  is  called  the  aberration 
qf  light.  Its  effect  is  to  cause  each  of  the  fixed  stars  to 
ascribe  an  apparent  annual  oscillation  in  a  very  small  w- 
bit.  The  nature  of  tlie  diq>laeement  may  bo  conceived 
of  in  the  following  way :  Suppose  the  earth  at  any  moment, 
in  the  coarse  of  its  annual  revolution,  to  be  moving  to- 
ward a  point  of  the  celestial  sphere,  which  we  may  call  P. 
Then  a  star  lying  in  the  direction  P  or  in  the  oj^posite  di- 
rection win  tuffer  no  displacement  whatever.  A  star  ly- 
ing in  any  other  direction  will  be  disphUsed  in  the  direc- 
tion of  the  point  P  by  an  an|^e  propoiti<»ial  to  the  sine  of 
its  angnlar  distance  from  P.  At  9Cr  fro^  P  the  dis- 
pUcement  will  he  a  maximum,  and  its  angular  amonnt 
will  be  snoh  that  its  tangent  will  be  equal  to  the  ratio  of 
the  velocity  of  the  earth  to  that  of  light.  If  ul  he  the 
"aberratiim"  of  (he  star,  and  P8itB  angular  distanoe 
from  the  point  P,  we  AaXt  have, 


tan  ^  =  -,  sin  P^, 

Vand  «  being  the  respective  veloeitieB  of  H^t  and  <tf  the 
earth. 


of  the  w»y  from  A 
y  on  the  rod.  Con- 
Ilappeartobepoint- 
the  pointing  will  not 
at  will  deviate  from 

is  the  ratio  of  the 
carried  along  to  the 
liat  the  motion  of  the 

a  ray  of  light.  If 
>lve  hia  velocity  into 

to  the  ray  and  one 
lect  the  apparent  di- 
sfore  depend  entirely 

jrent  displacement  of 
1  called  the  aberratim 

of  the  fixed  atan  to 
m  in  a  very  amall  or- 
int  may  be  conceived 
a  earth  at  any  moment, 
ition,  to  be  moving  to- 
whioh  we  may  call  P. 
P  or  in  the  oppoaite  di- 
whatever.  A  atar  ly- 
diipUoed  in  the  direc- 
iportional  to  the  aine  of 

M*  iroiA  P  the  dia- 
id  its  angular  amount 
B  eqnalto  the  ratio  of 
irf  light.  If  ^  be  the 
'5it8  angular  diatanoe 


PS. 

dtiea  of  Uj^t  and  of  the 


vniooitT  Of  umiT. 


«4d 


Kow,  if  the  atar  liea  near  the  polo  of  the  ecliptic,  its  di- 
rection will  always  be  nearly  at  right  angles  to  the  direc- 
tion in  which  tlie  earth  is  moving.  A  little  consideration 
will  show  that  it  will  seem  to  describe  a  circle  in  conse- 
quence of  aberration.  If,  however,  it  lies  in  the  plane  of 
the  earth's  orbit,  then  the  various  poinds  toward  which 
the  earth  moves  in  the  course  of  the  year  all  lying  in  the 
ecliptic,  and  the  star  being  in  this  same  plane,  the  appar- 
ent motion  will  be  an  oscillation  back  and  forth  in  this 
plane,  and  in  all  other  positions  the  apparent  motion  will 
be  in  an  ellipse  mori  and  more  flattei  ed  as  we  approach 
the  ecliptic. 

Velocity  of  Light. — The  amorii^.  of  aberration  can  be 
determined  in  two  ways.  If  wh  know  the  t^me  which 
light  requires  to  come  from  tho  snn  to  trc  earth,  a  simple 
calculation  will  enable  us  to  determinn  '  t.  i  ratio  between 
this  velocity  and  that  of  the  earth  ii  tis  orbit.  For  in- 
stance, suppose  the  time  to  498  seconds;  on  light 
will  cross  the  orbit  of  the  eti  th  i>*  996  seoondtt.  The  cir- 
cumference of  the  earth  being  found  by  multiplying  it:; 
diameter  by  8  •  1416,  we  thus  find  that,  on  the  suppoeitiuu 
we  have  made,  light  would  move  around  the  drcumior- 
ence  of  the  earth's  orbit  in  62  mmutes  and  8  seconds. 
But  the  earth  makes  this  aaire  circuit  in  866^  days,  and 
the  ratio  of  these  two  quantities  is  10090.  The  nazimum 
diaplaoement  of  the  star  by  aberration  will  therefore  be  the 
angle  of  which  the  tangent  is  Trffvi  >nd  this  angle  we 
find  by  trigonmnetrical  calcn]ati<m  to  be  ao**  44. 

This  calenlation  presupposes  that  we  know  how  long 
light  requires  t^  come  frmn  the  sun.  This  is  not  known 
with  great  aorivy;  owing  to  the  unavoidable  enrora  with 
which  the  obaerva^ona  of  Jupiter**  satellites  are  affected. 
It  is  therefore  more  usual  to  reverse  the  process  and  de- 
termine th"  diaplaoement  of  tiie  stars  by  direct  obaerva- 
tioo,  and  then,  by  a  calculation  the  nf9va»  of  that  we 
h«V6  lust  made,  to  determijoe  tlie  time  required  by  lof^t 
to  reMh  us  from  the  snn.    Many  patnatakiog  detiermina- 


itWTnrvftwtrf'rf'*^ 


244  ASTttOKOitr, 

r^J  deviate  from  20-.«  by  n.o«  tlmn  two  or  three 
'"■tt;^fS."^o^iS°i  bydetem-ining  th.«>n^of 
.b^^L  or  by  ob^rving  the  -"iT?' *' "w  ^^ 

irZil^^^f  the  Bun,  we  may  obtain  the  vel<Kity  of 
uirbvStagitbym  But,  on  the  other  hand,  a  we 
'ideteTne^wmLy  miles  light  mov« ma  seo^^ 
r  tS  infer  the  distance  of  the  «m  ^y  ™5^^22S<^ 
Z  the  same  factor.  During  «^«.lf  ^^^'^^  t^*^^ 
of  the  aun  was  found  to  be  certainly  between  90  and  100 
^S^rSmUes.  It  was  therefore  c<««cayoondud^ 
Cthe  velocity  of  light  was  somet^leBB  th«^^»0O0 

mL  ner  second,  and  probably  between  180,000  and 
^"XSvtiocityhL  since  boen  dete^ned  moj. 

exactly  by  the  direct  measurements  at  the  surface  of  the 

earth  abready  mentioned. 


ie  since  the  time  of 
e  may  say  that  the 
1,"  as  it  is  called,  is 
tiechancesarethatit 
e  than  two  or  three 

ning  the  constant  of 
ies  of  the  satellites  of 
ired  for  light  to  pass 
»nnot  thus  determine 
how  far  the  sun  is. 
^  and  the  distance  of 
,  can  infer  the  other, 
he  time  required  for 
seconds,  a  time  which 
second.    Then  know- 
obtain  the  velocity  of 
tt  the  other  hand,  i|  wo 
moves  in  a  second,  we 
J  sun  by  multiplying  it 
at  century  Uie  distance 
iy  between  90  and  100 
re  correctty  oonolnded 
thing  less  than  ^)0,000 
between  180,000  and 
boen  determined  more 
Lts  at  the  surf  ace  of  the 


CHAPTER  XI. 

CHRONOLOGY. 

%  1.    ASTBONOMIOAI.  MSASXTBEBQ  OF  TDOS. 

The  most  intimate  relation  of  astronomy  to  the  daily 
life  of  mankind  has  always  arisen  from  its  affording  the 
only  reliable  and  accurate  measure  of  long  intervals  of  time. 
The  fundamental  units  of  time  in  all  ages  have  been  the 
day,  the  mouth,  and  the  year,  the  first  being  mensured  by 
the  revolution  of  the  earth  on  its  axis,  the  seccmd,  prim- 
itively, by  that  of  the  moon  around  the  earth,  and  the  third 
by  that  <^  the  earth  round  the  sun.  Ilad  the  natural  month 
consisted  of  an  exact  entire  number  of  days,  and  the  year 
of  an  exact  entire  number  of  months,  there  would  have 
been.no  history  of  the  calendar  to  write.  There  being  no 
such  exact  relations,  innumerable  devices  have  been  tried 
ior  amoothlng  off  tlie  difficulties  thus  arising,  the  mere 
description  of  which  would  fill  a  volume.  We  shall  en- 
deavor to  give  tlie  reader  an  idea  of  the  general  characto' 
of  these  devices,  including  those  from  which  our  own  cal- 
eadu  ori^nated,  witiiout  wearying  him  by  the  introduc- 
tion of  tedUnu  details. 

Of  the  three  units  of  time  just  mentioned,  the  moet  nat- 
ural and  starring  is  the  shortest— namely,  the  day.  park- 
ing aa  it  does  the  regular  ahemations  of  wakefohn^  and 
rest  for  both  man  and  animab,  no  artronomioal  obeerva- 
tions  were  Mceasary  to  its  recognition.  It  is  so  neariy 
unifcMrm  in  Imgthtiiatthe  most  refined  astroiuMnical  ohmf- 
vatioas  of  modem  times  have  nover  certainly  indicated 


246  A8TB0N0MT. 

any  change.  This  uniformity,  and  ita  entire  freedom  from 
all  ambiguity  of  meaning,  have  always  made  the  day  a 
common  fundamental  unit  of  astronomers.  Except  for 
the  inconvenience  of  keeping  count  of  the  great  number 
of  days  between  remote  epochs,  no  greater  umt  would 
ever  have  been  necessary,  and  we  might  all  date  our  let- 
ters by  the  number  of  days  after  Chmst,  or  after  a  sup- 
posed epoch  of  creation.  , 

The  difficulty  of  remembering  great  numbers  is  sucli 
that  a  longer  unit  is  absolutely  necessary,  even  in  keeping 
the  reckoning  of  time  for  a  single  generation.     Such  a 
unit  is  the  year.   The  regukr  changes  of  seasons  in  all  ex- 
tra-tropical latitudes  renders  tliis  unit  second  only  to  the 
day  in  the  prominence  with  which  it  must  have  struck  the 
minds  of  primitive  man.     These  changes  are,  how^ever,  so 
slow  and  ill-marked  in  their  progress,  that  it  would  have 
been  scarcely  possible  to  make  an  accurate  detenmnation 
of  the  length  of  the  year  from  the  observation  of  the  sea- 
sons      Here  astronomical  observations  came  to  the  aid  ot 
our  progenitors,  and,  before  the  beginning  of  extant  his- 
toryfit  was  known  that  the  alternation  of  seasons  was  due 
to  the  varying  declination  of  th«  sun,  as  the  latter  seemed 
to  perform  its  annual  course  among  the  stars   m  tiie 
«  obUque  circle"  or  ecUptic.  The  common  people,  who  did 
not  understand  the  theory  of  the  sun's  motion,  knew  that 
certain  seasons  were  marked  by  the  position  of  certain 
bright  stars  rehitively  to  the  sun-that  is,  by  those  stare 
ristog  or  setting  in  the   morning  or   evemng  twiOight. 
Thus  arose  two  methods  of  measuring  the  length  of  the 
year— the  one  by  the  time  when  the  son  crossed  the  eqm- 
noxes  or  Botedoes,  the  other  when  it  seemed  to  pass  a  cer- 
tain  point  among  the  stars.     As  we  have  already  exphun- 
ed,  these  yea»  were  slightly  diflfeient,  owmg  to  the  p»- 
ceidon  of  the  equinoxes,  theHrst  or  equmoct«l  year  being 
alittle  less  and  the  second  or  sidereal  year  a  litfle  g«»ater 

than  865J  d*y*  ^   i*  ^ 

Themunberof  days  in  a  year  is  too  great  to  admttol 


OHRONOLOQT. 


247 


entire  freedom  from 
yg  made  the  day  a 
omers.  Except  for 
►f  the  great  number 
greater  unit  would 
ght  all  date  our  let- 
[M8T,  or  after  a  Bup- 

3at  numbers  is  such 
Eiry,  even  in  keeping 
generation.     Such  a 
\  of  seasons  in  all  ex- 
t  second  only  to  the 
must  have  struck  the 
iges  are,  however,  so 
,  that  it  would  have 
[•urate  determination 
bservation  of  the  sea- 
ls came  to  the  aid  of 
inning  of  extant  bis- 
on of  seasons  was  due 
I,  as  the  latter  seemed 
»ng  the  stars   in  the 
nmon  people,  who  did 
I's  motion,  knew  that 
le  poeition  of  certain 
that  is,  by  those  stwu 
or   evening  twilight, 
[ng  the  length  of  the 
)  ran  crossed  the  equi- 
seemed  to  paw  a  cer- 
)  have  already  explain- 
nt,  owing  to  the  pie- 
>  equinoetittl  year  bmng 
Mdyetfalitae  gcmter 

too  great  to  •dmHof 


their  being  easily  remembered  without  any  break ;  an  in- 
termediate period  is  therefore  necessary.  Such  a  period 
is  measured  by  the  revolution  of  the  moon  around  the 
earth,  or,  more  exactly,  by  the  recurrence  of  new  moon, 
which  takes  place,  on  the  average,  at  the  end  of  nearly 
2di  days.  The  nearest  round  number  to  this  is  30  days, 
and  12  periods  of  30  days  each  only  lack  5^  days  of  being 
a  year.  It  has  therefore  been  common  to  consider  a  year 
as  made  up  of  12  months,  the  lack  of  exact  correspondence 
being  filled  by  various  alterations  of  the  length  of  the 
month  or  of  the  year,  or  by  adding  surplus  days  to  each 
year. 

The  true  lengths  of  the  day,  the  month,  and  the  year 
having  no  common  divisor,  a  difficulty  arises  in  attempting 
to  maJke  months  or  days  into  years,  or  days  into  months, 
owing  to  the  fractions  which  will  always  be  left  over.  At 
the  same  time,  some  rule  bearing  on  the  subject  is  necessary 
in  order  that  people  may  be  able  to  remember  the  year, 
month,  md  day.  Such  roles  are  found  by  choosing  some 
oyde  or  period  whidi  is  very  nearly  an  exact  number  of 
two  units,  of  months  and  of  days  for  example,  and  by  di- 
viding this  cycle  up  as  evenly  as  possible.  The  principle 
on  which  this  is  d<me  can  be  seen  at  once  by  an  example, 
for  which  we  shall  choose  the  lunar  month.  The  true 
length  of  this  month  is  a9-580&884  days.  We  see  that 
two  of  these  months  is  only  a  little  over  69  days ;  so,  if 
we  take  a  cy<de  of  69  days,  and  divide  it  into  two  months, 
the  one  of  80  and  tiie  other  of  29  days,  we  shall  have  a 
first  approximation  to  a  true  average  month.  But  onr 
cyde  will  be  too  short  by  O'  •  061,  the  excess  of  two  months 
over  69  days,  and  this  error  will  be  added  at  the  end  of 
every  cycle,  and  thus  go  on  increasing  as  long  as  Ihe  cycle 
is  used  without  ohaage.  At  the  end  of  16^cyoles,  or  of 
32  lunar  m<niths,  tlie  aocnmulated  error  will  amount  to 
one  day.  At  the  end  of  this  time,  if  not  sooner,  we 
alMNdd  have  to  add  a  day  to  one  of  the  months. 

Wiling  that  we  shall  uhimatelj  be  wrong  if  we  hav<>  a 


ii'UiJanilliMH 


248 


ASTRONOMY. 


two-month  cyde,  we  seek  for  a  more  exact  one.    Each 
month  of  30  days  is  nearly  0*.47toolong,  and  eadi  monfli 
of  29  days  is  rather  more  than  0*  •  68  too  short.    Bo  m  the 
lonir  run  the  months  of  30  days  ought  to  be  more  numw- 
om  than  those  of  29  days  in  the  ratio  that  63  bears  to 
47,  or,  more  exactly,  in  the  ratio  that  -6306884  bears  to 
.  4694116.    A  close  approximation  will  be  had  by  having 
the  long  months  one  eighth  more  numerous  than  the  diort 
ones,  the  nnmbers  in  question  being  nearly  in  the  ratio  of 
9  : 8.    So,  if  we  take  a  cycle  of  17  months,  9  long  and  8 
short  ones,  we  find  that  9x30  +  8x29  =  602  days  for 
the  assumed  length  of  our  cycle,  whereas  the  true  length 
of  17  months  is  very  near  602*.0200.    The  error  will 
therefore  be  -02  of  a  day  for  every  cyde,  and  wiH  not 
amount toaday  till  the  end  of  60  cydes,  or  nearly  70 

^Titill  nearer  approadi  will  be  found  by  taking  a  qjde 
of  49  months,  26  to  be  long  and  23  Aoit  ones.    These 
49   months  ^iU  be  composed  of   a«^;;  «>  +  28  x  29  = 
1447  days,  whereas  49  true  lunar  months  will  eompnse 
1446.998882  days.    Eadi  cycle  will  therefow  be  too  long 
by  only  -001168  of  a  day,  and  the  error  would  n«t«jmo^t 
to  a  day  tai  the  end  of  84  cydes,  or  more  th«j  8000  y«ffl^ 
Although  these  cycles  are  so  near  the  truth,  ihgr  oorfd 
not  be  Ld  with  convenience  be«u«e  Aey  ^^^^ 
at  different  thnes  of  the  year.    The  problem  is  therefore 
to  find  a  cyde  whidi  shall  comprise  an  entire  n^^^er  of 
years.    We  shall  see  hereafter  what  solutions  of  this 
problem  were  actually  found. 


§  2. 


lOBKATIOV  or  GAXOHDABt. 


The  months  noW  or  heretofore  in  ™«  •'^^.P^^'jJ" 
of  the  globe  may  for  the  mort  part  be  divided  mto  two 

''^The  lunar  month  pure  and  simple,  or  the  mean 
interval  between  sttcoeottve  new  moons. 


9  exact  OBe.    Each 


>ng,  and  eadi  month 

00  short.  80  in  the 
to  be  more  numer- 
tio  that  58  bears  to 

1  .5305884  bean  to 
ill  be  had  by  having 
lerouB  than  the  short 
learly  in  the  ratio  of 
uontiis,  9  long  and  8 
<  29  =  502  days  for 
)reasthe  true  length 
!00.    The  error  will 

cycle,  and  will  not 
cycles,  or  nearly  70 

ad  by  taking  a  cycle 
18  short  ones.  These 
26x80  +  28x39  = 
nonthswill  comprise 
therefore  be  too  long 
ror  would  not  amonnt 
aore  than  8000  years, 
the  truth,  ih^  could 
ise  they  would  begin 
>  problem  is  therefore 
)  an  wtire  number  of 
tiat  sdntionB  of  this 


ase  amwig  A»  P«o0« 
t  be  divided  into  two 

simple,  or  the  mean 
ons. 


THB  OALBNDAR 


(2.)  An  approximation  to  the  twelfth  part  of  a  year, 
without  req>ect  to  the  motion  of  the  moon. 

The  Lunar  Month. — The  mean  interval  between  con- 
secutive new  moons  being  nearly  29^  days,  it  was  common 
in  the  use  of  the  pure  lunar  month  to  have  months  of  29  and 
30  days  alternately.  This  supposed  period,  however,  as  just 
shown,  will  fall  short  by  a  day  in  about  2|  years.  This  de- 
fect was  remedied  by  introducing  cycles  containing  rather 
more  months  of  80  than  of  29  days,  the  small  excess  of 
long  months  being  spread  uniformly  through  the  cycle. 
Thus  the  Greeks  had  a  cycle  of  235  months  (to  be  soon 
described  more  fully),  of  which  125  were  full  or  long 
months,  and  110  were  short  or  deficient  ones.  We  see 
that  the  length  of  this  cycle  was  6940  days  (125  x  30  + 
110  X  29),  whereas  the  length  of  235  true  lunar  months 
is  235  X  29  •  53088  =  6939  •  688  days.  The  cycle  was  there- 
fore too  long  by  leas  than  one  third  of  a  day,  and  the  error 
of  count  would  amount  to  only  one  day  in  more  than  70 
years.  The  Mohammedajos,  again,  took  a  cycle  of  360 
months,  which  they  divided  into  169  short  and  191  long 
ones.  The  length  of  this  cyde  was  10631  days,  while  the 
true  length  of  360  lunar  months  is  10631  •  012  days.  The 
count  would  therefore  not  be  a  day  in  error  until  the  end  of 
about  80  cycles,  or  nearly  23  centuries.  This  month  there- 
fore follows  the  moon  closely  enough  for  all  practical  pur- 
poses. 

MmaXbB  othmr  than  Lunar.— The  complications  of  the 
system  just  described,  and  the  consequent  difficulty  of 
making  the  calendw  month  represent  the  course  of  the 
moon,  are  so  gr^  At  that  tiie  pure  lunar  month  was  gen- 
erally abandoned,  except  among  people  whose  religion  re- 
quired importuit  ceremonies  at  the  time  of- new  moon. 
In  cases  of  such  abandmiment,  the  year  has  be«i  usually 
divided  into  12  montiis  of  sli^^tly  different  lengths.  The 
ancient  Egyptians,  however,  had  19  months  of  80  days 
each,  to  whidi  they  added  5  snpplfanentary  days  at  the 
dose  <rf  each  year. 


l!i„'li>lillllMili'lil  I «»;!»!«»»««»>•»"»»■»"•»"" 


WMMti 


350 


A8TR0N0MT. 


Kinds  of  Tear.— As  we  find  two  different  syBtems  of 
months  to  have  been  used,  bo  we  may  divide  the  calendar 
years  into  three  classes— namely  : 

(1.)  The  lunar  year,  of  12  Innar  months. 

(2.)  The  solar  year. 

(8.)  The  combined  Inni-solar  year. 

The  Lunar  Tear.— We  have  already  called  attention  to 
the  f  Mt  that  the  time  of  recurrence  of  the  year  is  not  weU 
marked  except  by  astronomical  Phenomena  which  the 
casual  observer  would  hardly  remark.  But  the  tame  of 
new  moon,  or  of  beginning  of  the  month,  is  always  weU 
marked.  Consequently,  it  was  very  natural  for  people  to 
begin  by  considering  the  year  as  made  up  of  twelve  luna- 
tions, the  error  of  eleven  days  being  unnotic«ible  ma 

singte  year,  unless  careful  astronomical  o^^^^^J^^J^fJ 
m.Se.    Even  when  thiserrorwas  fully  recogmzed,itimght 

be  considered  better  to  use  the  regular  year  of  12  lunar 
months  than  to  use  one  of  an  irregular  or  varymg  number 
of  months,  f-hayearis^erehg^us^^^^^^^^ 
hammedans  to  this  day.  Ihe  excess  oi  xx  uj- 
amount  to  a  whole  year  in  83  yews,  82  «>1«»!  y«*"  ^^ 
nearly  equal  to  33  lunar  years.  In  this  period  therefore 
^^B2>nwill  havecoirsed  through  ^times  of  ^e 
^.     The  lunar  year  has  therefore  been  caUed  the 

"  retlllf  C:lln  forming  this  year,  the  aUem^to 
measure  the  year  by  revolutions  of  the  moon  »  «^f«V 
Sdoned,  id  its  Lg^  "^Lt  T^^tlS^ 

length  has  been  known  to  ^^\^^^  ^^J^y^ 
tim^of  the  earliest  astronomera,  and  f^^^J^, 
in  our  calendar  of  having  tliree  yeamof  866  d^  «^«» 
lowed  by  one  of  m  days,  has  ^  ««^P^5^?^", 
from  the  remotest  hiirt«ric  times  T^J^,^^^ 
is  nowcalled  by  us  the  JWKon  r«r,  after  JiTUO.  Oi»A«, 

from  whom  we  obtained  it. 


THE  CALENDAR. 


361 


Lifferent  syBtems  of 
divide  the  calendar 

tntha. 


y  called  attention  to 
I  the  year  is  not  well 
momena  which    the 
:.    But  the  time  of 
lonth,  is  always  well 
natural  for  people  to 
le  up  of  twelve  luna- 
ig  unnoticeable  in  a 
•al  observationa  were 
f  recognized,  it  might 
liar  year  of  12  Innar 
UP  or  varying  number 
pons  one  of  theMo- 
seu  of  11  days  will 
83  solar  years  being 
this  period  therefore 
igh  all  times  of  the 
ore   been  called  the 

9  year,  ihe  attempt  to 
the  moon  in  entirely 
»  depend  entirely  on 
ar  year  thus  indicated 
d  modem  times.    Its 

r  866i  d»y»  from  ^ 
id  the  qrrtem  adopted 

Bof  SeSdiqrBrtcli^^p'- 
en  employed  in  CJhina 
This  ye«  al  36H  day" 
r,  after  J^uuvs  0 jmab, 


The  lAiii4kdar  Tear. — If  the  lunar  months  must,  in 
some  way,  be  made  up  into  solar  years  of  the  proper  av- 
erage length,  then  these  years  must  be  of  unequal  length, 
some  having  twelve  months  and  others  thirteen.  Thus,  a 
period  or  cycle  of  eight  years  might  be  made  up  of  99 
lunar  months,  6  of  the  years  having  12  months  each,  and 
3  of  them  18  months  each.  Such  a  period  would  comprise 
2928i  days,  so  that  the  average  length  of  the  year  would 
be  865  days  10^  hours.  This  is  too  great  by  about  4  hours 
42  minutes.  This  very  plan  was  proposed  in  ancient 
Oreeoe,  but  it  was  superseded  by  the  discovery  of  the 
MeUmio  Oyde,  which  figures  in  our  church  calendar  to 
this  day.  A  luni-solar  year  of  this  general  diaracter  was 
also  used  by  the  Jews. 

The  MMonio  Qyole. — The  preliminary  considerations  we 
have  set  forth  will  now  enable  us  to  understand  the  origin 
of  our  own  calendar.  We  begin  with  the  Metonic  Cycle 
of  the  ancient  Greeks,  which  still  regulates  some  religious 
festivals,  although  it  has  disappeared  from  our  civil  reck- 
oning of  time.  The  necessity  of  employing  lunar  months 
caused  the  Greeks  great  difficulty  in  regulating  their  cal- 
endar so  as  to  accord  '«rith  their  rules  for  religious  feasts, 
until  a  solution  of  the  problem  was  found  by  Mkton,  about 
488  B.O.  The  great  discovery  of  Mbton  was  that  a  period 
or  cyde  of  6940  days  could  be  divided  up  into  235  lunar 
months,  and  also  into  19  sohu*  yean.  Of  these  months, 
125  were  to  be  of  80  days  each,  and  110  of  29  days  each, 
which  wonld,  in  all,  make  up  the  required  6940  days.  To 
see  how  nearly  this  rule  represents  the  actual  luotions  of 
the  ann  a^d  moon,  we  remiark  that : 


M6  lunations  require  6989 

l»JuliMiyetn  "  6989 

19  tmesolar  years  require    6989 


Huan.  MlB. 

la  81 

18  0 

14  27 


We  aee  that  thon^  the  cyde  of  6940  dajs  is  a  few  hours 
toQ^kng,  yet,  if  we  take  985  true  lomr  mimths,  we  find 


252  ASTRONOMY. 

aew  duv.  Mch,  md  .  Utile  more  than  W  true  •oto  yem. 
T^bZ.no,»w«t.Uk,tl««a85m.nth.jnddmd= 

««fl«»l  on  mbUc  montunente  in  letter,  of  gold.     Ibo  rule 
^  Mng  *e  golden  nnmbe,  i.  to  divid^he  nj«nb.r  o 
the  ycT  b,  19,  «.d  .dd  1  to  the  -"J^; ,!^  ^ 

to  1899  it  ,n.jbe  fonnd  by  ""Ply  "■*t^2  forS 
ftoye«.    It  i.  employed  in  onrehnrehcdendK  for  and 

inc  the  time  of  Ewter  Bnnd«y.  , 

*l.riod  of  <«1T,«..-We  have  •«»;,*",*•  jtn^ 
8940  dam  i«  a  few  honr.  too  long  either  for  886  Innar 
WtoOTforWwtaryeara.  CAU.r,.»  therefM. ««.^t 
7^^  it  by  taW.*  on.  day  o«  of  ^^i^  ^S 
TO  that  the  fonr  cyde.  Aonld  h««  S"6»  dayj  wm™ 
"ere  to  be  divided  into  940  month.  Kid  int.  W  y»». 
^Lveamwonldthaihe  Jnli».  ye«»,  wM.  the  ^^ 

he  would  iMtTe  been  yet  newrter  **»«  *™*^,,    ^^_^_„k. 
able  calendwiirhicb  bare  '*^«»«d  JL"^^  Jf2i^ 


THK  MOHAMMEDAN  CALENDAR. 


368 


uilOJvliuiyeanof 
19  true  sokr  years. 
5  months  and  divide 
mid  have  12  months 
The  long  years, 
those  corresponding 
19,  while  the  first, 
years.  In  general, 
smately,  bnt  it  was 
or  a  short  one  every 
jTcle  there  should  be 

the  number  of  the 
I  to  owe  itsappella- 
s  over  Mkton's  dis- 
ed  the  division  and 
r  calendar  to  be  in- 
■B  of  gold.     The  mle 
livide  the  number  of 
oainder.     From  1881 
abtractmg  1880  from 
irch  calendar  for  find- 
en  that  the  ejrde  of 
either  for  286  lunar 
TPUs  therefore  sought 
of  every  fourth  jgrde, 
re  27769  days,  which 
IS  and  into  76  years, 
ears,  while  the  raenr- 
X  hours  in  error  at  the 
en  a  day  from  every 
1  month  of  ^t  <r)rcle, 
truth. 

mong  tbe  most  remark- 
in  use  to  the  pnnnt 
The  yew  ii  oovnogd 


of  12  lunar  months,  and  therefore,  as  already  mentioned, 
does  not  correspond  to  the  course  of  the  seasons.  As  with 
other  systems,  the  problem  is  to  find  such  a  cycle  that  an 
entire  number  of  these  lunar  yean  shall  correspond  to  an 
integral  number  of  days.  Multiplying  the  length  of  the 
IxsMX  month  by  12,  we  find  the  true  length  of  the  lunar 
yeu'  to  be  864-86706  days.  The  fraction  of  a  day  being 
not  far  from  one  third,  a  three-year  cycle,  comprising  two 
years  of  864  cud  one  of  866  days,  would  be  a  first  approx- 
imation to'  three  ^unar  years,  but  would  still  be  one  tenth 
of  a  day  too  short.  I::  tc  such  cycles  or  thirty  years, 
this  deficiency  would  amount  to  an  entire  day,  and  by  add- 
ing the  day  at  the  end  of  each  tenth  three-year  cycle, 
a  very  near  approach  to  the  true  motion  of  the  moon 
will  Im  obtained.  This  thirty-year  cycle  will  consist  of 
10681  days,  while  the  true  length  of  860  lunar  months  is 
10681  •  01 16  days.  The  error  will  not  amount  to  a  day  until 
the  end  of  87  cycles,  or  2610  yean,  so  that  this  system  is 
accurate  enough  for  all  practiMl  purposes.  The  common 
Mohammedan  year  of  354  days  is  composed  of  months 
containing  alternately  80  and  29  days,  the  first  having 
80  and  the  hst  29.  In  the  years  of  866  days  the  alter- 
nation is  the  same,  except  that  one  day  is  added  to  the  last 
month  of  the  yesr. 

The  <dd  custom  was  to  take  for  the  first  day  of  the 
m<mth  that  following  the  evening  on  which  the  new  moon 
oould  first  be  seen  in  the  west.  It  is  said  that  before  the 
exact  arrangement  of  the  Mohammedan  calendar  had  been 
oomjdeted,  the  nde  was  that  the  visibility  of  the  ereaeent 
moon  should  be  certified  by  the  testimony  of  two  wit- 
nesses. The  time  of  new  moMH  given  in  our  modem 
almanacs  is  that  when  the  moon  passes  neariy  between  us 
and  the  mn,  and  is  therefore  entirely  invisiUe.  The  moon 
is  generally  <me  or  two  days  old  before  it  can  be  seen  in  the 
eveofaig,  and,  in  conseqnoioe,  the  lunaf  moitili  of  the  Mo- 
hammedaM  and  of  othemoomuMooes  about  two  daya  after 
«ilui.iOtiia]  aLDUue  time  of  new  ibo<ml 


'MMMHIMHMiiliMtaiMMMHH 


9M 


A8TB0N0MT. 


The  civil  calendar  now  in  use  throuKhoot  Christendom 
had  its  origin  among  the  Romans,  and  its  foundation  was 
laid  by  Jcuus  Cjbbar.  Before  his  time,  Rome  can  hardly  be 
said  to  have  had  a  chronological  system,  the  length  of  the 
year  not  being  prescribed  by  any  invariable  rule,  and  be- 
ini^  therefore  changed  from  time  to  time  to  suit  the  caprice 
or  to  compass  the  ends  of  the  rulers.  Instances  of  this 
tampering  disposition  are  familiar  to  the  historical  student. 
It  is  said,  for  instance,  that  the  Gauls  having  to  pay  a 
certain  monthly  tribute  to  the  Romans,  one  of  the  govern- 
ors  ordered  the  year  to  be  divided  into  14  months,  in 
order  that  the  paydays  might  recur  more  rapidly.  To 
remedy  this,  CjBbab  odled  in  the  aid  of  Sosiobnes,  an  as- 
tronomer of  the  Alexandrian  school,  and  by  them  it  was 
arranged  that  the  year  should  consist  of  865  days,  with  the 
addition  of  one  day  to  every  fourth  year.  The  old  Roman 
months  were  afterward  adjusted  to  the  Julian  year  in 
such  a  way  as  to  give  rise  to  the  somewhat  irreguUr 
arrangement  of  months  which  we  now  have. 

Old  and  Hew  Styles. — The  mean  length  of  the  Julian 
year  is  866|  days,  about  11^  minutes  greater  than  that  of 
the  true  equinoctial  year,  which  measures  the  rwurrenoe 
of  the  seasons.  This  difference  is  of  little  practical  im- 
portance, as  it  only  amotmts  to  a  week  in  a  thousand  years, 
and  a  change  of  this  amount  in  that  period  is  productive 
of  no  inconvenience.  But,  desirous  to  have  the  year  as 
correct  as  possible,  two  duu^raB  were  introduced  into  the 
calendar  by  Pope  Gbbqoby  XIII.  with  this  object.  They 
were  aa  follows : 

1.  The  day  following  October  4, 1689,  waa  callf^  the 
15th  instead  of  the  5th,  thoa  advancing  the  count  10  days. 

a.  The  doeing  year  of  each  oentory,  1600,  1700,  etc., 
instead  of  being  always  a  leap  year,  aa.  in  the  Julian 
calendar,  is  such  (miy  when  the  number  of  the  cnntuiy  is 
divisible  by  4.  Thus  while  1600  remained  a  kap  year,  as 
before,  1700, 1800,  and  1900  wen  to  be  common  yean. 

This  change  in  the  calendar  was  speedily  adopted  hy0^ 


THE  CALKNDAR. 


255 


[toot  Christendom 
tB  foundation  wm 
;onie  can  hardly  be 

the  length  of  the 
ftble  rule,  and  be- 
to  suit  the  caprice 

Instances  of  this 
historical  student. 

having  to  pay  a 
[>ne  of  the  govem- 
tto  14  months,  in 
aore  rapidly.     To 

SoBiOENES,  an  as- 
id  by  them  it  was 
866  days,  with  the 
.  The  old  Boman 
he  Julian  year  in 
omewhat  irregukr 
have. 

Qgth  of  the  Julian 
reater  than  that  of 
iree  the  rAnirrenoe 
little  practical  im- 
n  a  thousand  years, 
leriod  is  productive 
\  have  the  year  as 
introduced  into  the 
I  this  object.    They 

L682,WMcaUKl  the 
I  the  count  10  days. 
y,  1600, 1700,  etc., 
,  as.  in  the  Julian 
)er  of  the  century  is 
Bined  a  leap  year,  as 
be  common  yean, 
ledily  adopted  by  t^ 


Catholic  countries,  and  more  slowly  by  Protestant  ones, 
England  l.olding  out  until  1762.  In  Rwsia  it  has  never 
been  adopted  at  all,  Uie  JuUau  calendar  being  stiU  con- 
tinned  without  change.  The  Russian  reckoning  is  there- 
fore 12  days  behind  ours,  the  ten  days  dropped  m  1682 
being  increased  by  the  days  dropped  from  the  years  17iM) 
and  1800  in  the  new  reckoning.  This  modified  calendar 
is  called  the  Or^n(mtm  Calendar,  or  JVew  Style,  while  tiie 
old  system  is  cai.od  the  Julian  Calendar,  or  Old  Style. 

It  is  to  be  remarked  that  the  practice  of  commencing 
the  year  on  January  1st  was  not  universal  until  compara- 
tively recent  times.  During  the  first  sixteen  centuries  of 
the  JuUan  calendar  there  was  such  an  absence  of  definite 
rules  on  this  subject,  and  snch  a  variety  of  practice  on  the 
part  of  different  powers,  that  the  simple  enumeration  of 
the  times  chosen  by  various  governments  and  pontiffs  for 
the  commencement  of  the  year  would  make  a  tedious 
chapter.  The  most  common  times  of  commencing  were, 
perhaps,  March  1st  and  March  22d,  the  latter  being  the 
time  of  the  vernal  equinox.  But  January  1st  gradually 
made  its  way,  and  became  universal  after  its  adoption  by 
England  in  1762. 

Bolar  Oyole  and  Dominioal  Letter.— In  our  church  cal- 
endars January  1st  is  marked  by  the  letter  A,  January  2d 
by  B,  and  so  on  to  G,  when  the  seven  lettere  begm  over 
again,  and  are  repeated  through  the  year  in  the  same 
order.  Each  letter  there  indicates  the  same  day  of  the 
week  throughout  each  separate  year,  A  indicating  the  day 
on  which  January  1st  falls,  B  the  day  foUowing,  and  so 
on.  An  exception  occurs  in  leap  years,  when  February 
S9th  and  March  Ist  are  marked  by  the  same  letter,  so  that 
a  diange  occurs  at  the  beginning  of  Mardi.  The  letter 
corresponding  to  Sunday  on  this  scheme  is  iBalled  the  Jkh 
mmiotd  or  Sunday  lottef^  and,  when  we  once  know  what 
letter  it  is,  all  the  Sundftjs  of  the  year  are  indicated  by 
that  letter,  and  hence  all  the  other  days  of  the  week  by 
^bmr  letters.     In  leap  years  there  wUl  be  two  Dominioal 


i^^itm 


fB6 


ASTRONOMY. 


lettere,  that  for  the  Iwt  ten  months  of  the  year  being  the 
one  next  preceding  the  letter  for  January  and  Febniary. 
In  the  Julian  calendar  tlie  Dominical  letter  must  alway» 
recur  at  the  end  of  28  yean  (beaidea  three  "^"ff «««;»* 
unequal  interval,  in  the  mean  time).  This  period  is  called 
the  wi«r  cycle,  and  determines  the  days  of  the  week  on 
which  the  days  of  the  month  fall  during  each  year. 

Since  any  day  of  the  year  occur*  one  day  earUer  m  the 
week  than  it  did  the  year  before,  or  two  days  earlier  when 
a  29th  of  February  has  intervened,  the  Dominical  letters 
mmr  in  the  order  G,  F,  E,  D,  C,  B,  A,  G,  etc.    A 
simihff  fact  may  be  expressed  by  saying  that  any  day  ol 
the  year  occur*  one  day  kter  in  the  week  for  every  year 
that  has  eUipsed,  and,  in  addition,  one  day  later  for  eveir 
29th  of  February  that  has  intervened.    This  fact  wiU  make 
it  easy  to  calcuhte  the  day  of  the  week  on  which  any  his- 
torici  event  happened  from  the  day  corresponding  in  any 
past  or  future  year.    Let  us  take  the  f ollowmg  example  : 
On  what  day  of  the  week  was  Washwoton  bom,  the 
date  being  1782,  February  22d,  knowing  that  February 
22d,  1879,  feU  on  Satmrday.    The  interval  is  147  yean : 
dividing  by  4  we  have  a  quotient  of  86  and  a  remainder 
of  8.  showing  that,  had  every  fourth  year  m  the  interval 
been  a  leap  year,  there  were  either  86  or  87  leap  yean. 
As  a  February  29th  followed  only  a  week  after  the  date, 
the  nmnber  must  be  87  ;•  but  as  1800  was  dropped  from 
the  Hat  of  leap  yean,  the  number  was  leaUy  only  86. 
Then  147  +  86  =  188  days  advanced  m  the  week,    in- 
riding  by  7,  becau«»  the  same  day  of  the  w«*  rwun 
afterleven  days,  we  find  a  remainder  of  1.    So  Febru«y 
22d.  1879,  is  one  day  further  advanced  than  was  iebmary 
22d,  1782 ;  so  the  former  being  Saturday,  WASHWoroir 
was  bom  <m  Friday.  .  .,_ 

•  PBihapslhemort  cmiv«leBtw«raf  a*!*^/*^*?"-!!; 

S.  W  8C0UIB  iwtween  tto  two  dats^  only  •  we*  altar  aia  *(•». 


DIVISION  OF  THE  DAT 


367 


the  year  being  the 
itry  and  February, 
letter  uitiBt  always 
hree  recurrences  at 
'his  period  is  called 
ys  of  the  week  on 
ig  each  year. 
I  day  earlier  in  the 
o  days  earlier  when 
e  Dominical  letters 

B,  A,  G,  etc.  A 
ig  that  any  day  of 
eek  for  every  year 

day  later  for  every 
This  fact  will  make 
k  on  which  any  his- 
orreeponding  in  any 
following  example : 
kSHiHOTON  bom,  the 
nring  that  Febmary 
itervalis  147  years: 
86  and  a  remainder 
year  in  the  interval 
86  or  87  leap  yean, 
xreek  after  the  date, 
0  was  dropped  from 
was  really  only  86. 
i  in  the  week.    Di- 

of  the  week  reenn 

of  1.  So  Februaiy 
id  than  was  Febmary 
torday,  Washimgtov 


•riitoMMnotitfilMi^ 
MBlnterrMiM.  MitnMit> 
tav«  Fehfoary  M.  1878, 
ty  ft  wMk  afiar  ttw  iMk. 


I  8.  Diviuoir  or  ram  day. 

The  division  of  the  dny  into  hours  was,  in  ancient  and 
medinval  times,  effected  in  away  very  dififerent  from  that 
which  we  practice.  Artificial  time-keepers  not  being  in 
general  use,  the  two  fundamental  moments  were  sunrise 
and  sunset,  which  marked  the  day  as  distinct  from  the 
night.  The  first  subdivision  of  this  interval  was  marked 
by  the  instant  of  noon,  when  the  snn  was  on  the  meridian. 
The  day  was  thus  subdivided  into  two  parts.  The  night 
was  similarly  divided  by  the  times  of  rising  and  culmina- 
tion of  the  various  constellations.  Evripidks  (480-407 
B.O.)  makes  the  chorus  in  Rhetus  ask  : 

"  CHOBiit.— Whose  ii  the  guard  T   Who  takes  my  turn  T    Tk»  fir^ 

miOwi^  tkroutfi  heium.  Awake !  Why  do  you  detey  T  Awake  from 
your  beds  to  watch  t  See  ye  not  the  brUlhmcy  of  the  moon  T  Mom, 
mom  indeed  is  iqtproaching,  and  hiOur  Uon$^  Oefonntniting  ilan. " 
—The  Tragedies  of  Enripidea.  LlteraUy  Translated  by  T.  A.  Buckley. 
London :  H.  O.  Bcdu.    1854.    Vol.  i,  p.  888. 

The  interval  between  sunrise  and  sunset  was  divided 
into  twelve  equal  parts  called  hours,  and  as  this  interval 
varied  with  the  season,  tlie  length  of  the  hour  varied  also. 
The  night,  whether  long  or  short,  was  divided  into  hours 
of  the  same  character,  only,  when  the  night  hours  vere 
long,  those  of  the  day  were  short,  and  vice  vena.  These 
variable  hours  were  called  temporary  houre.  At  the  time 
of  the  equinines,  both  the  day  and  the  night  hours  were 
of  the  same  lengtii  with  those  we  use— namely,  the  twenty- 
fourth  part  of  the  day  ;  these  were  therefore  called  egui- 
noetial  houre. 

The  use  of  these  temporary  honn  was  intimately  an- 
ioaiated  with  the  time  of  be^^ing  of  the  day.  Instead 
of  commencing  the  dvil  day  at  midn^t,  as  we  do,  it  was 
fflMtwhary  to  oommenoe  it  at  sunset.  The  Jewish  &tbbath, 
for  inrtUice,  oommeneed  as  soon  as  the  smi  set  on  Friday, 
and  ended  when  it  set  on  Saturday.  This  made  a  more 
distiBotive  <!yviai<m  of  the  avtronomieal  day  than  that 


258 


A8TR0N0MT. 


whicli  we  employ,  and  led.  natnrally  to  considenng  the 
day  and  the  nigkt  as  two  distinct  periods,  each  to  be  di> 
vided  into  12  hours. 

So  long  as  temporary  hours  were  used,  the  beginning  of 
the  day  and  the  beginning  of  the  night,  or,  as  we  should 
call  it,  six  o'clock  in  the  morning  and  six  o'clock  in  the 
evening,  were  marked  by  the  rising  and  setting  of  the  sun ; 
but 'When  equinoctial  hours  were  introduced,  neither  sun- 
rise nor  sunset  could  be  taken  to  count  from,  because  both 
varied  too  much  in  the  course  of  the  year.  It  therefore 
became  customary  to  count  from  noon,  or  the  time  at 
which  the  sun  passed  the  meridian.  The  old  custom  of 
dividing  the  day  and  the  night  each  into  12  parts  was  con- 
tinued, the  first  12  being  reckoned  from  midnight  to 
noon,  and  the  second  from  noon  to  midnight.  The  day 
was  made  to  commence  at  midnight  rather  than  at  noon 
for  obvious  reasons  of  convenience,  although  noon  was  of 
course  the  point  at  which  the  tune  had  to  be  determined. 

Bquatlon  of  Time. — To  any  one  who  studied  the  annual 
motion  of  the  sun,  it  must  have  been  quite  evident  that 
the  intervals  between  its  successive  passages  over  the 
meridian,  or  between  one  noon  and  the  next,  could  not 
be  the  same  throughout  the  year,  because  the  apparent 
motion  of  the  sun  in  right  ascension  is  not  constant.  It 
will  be  remcirbered  that  the  apparent  revolution  of  the 
starry  sphere,  or,  which  is  the  same  thing,  the  diurnal 
revolution  of  the  earth  upon  its  axis,naay  be  r^;arded 
as  absolutely  constant  for  all  practical  purpows.  This  rev- 
olution is  measured  around  in  rig^t  asoendon  as  explained 
in  the  opening  chapter  of  this  work.  If  the  sob  inereased 
its  right  ascension  by  the  sameamounieveiy  day,  H  would 
pass  the  meridian  8'  66'  later  every  day,  as  measi|rad  by 
sidereal  time,  and  hence  the  intervals  between  saooeirive 
passages  would  be  equal.  But  the  mod<m  of  the  nm  in 
right  ascension  is  unequal  firom  two  earnes :  (1)  the  un- 
equal motion  of  the  earth  in  its  annual  rMUJttttion  arouad 
it,  arising  from  the  eocentridty  of  the  oriiit,  and  (d)  Om 


APPARENT  AND  MEAN  TIME. 


259 


to  considenng  the 
odS)  each  to  be  di- 

jd,  the  beginning  of 
it,  or,  as  we  should 
I  six  o'clock  in  the 
1  setting  of  the  sun; 
dnoed,  neither  sun- 

from,  because  both 

year.    It  therefore 
on,  or  the  time  at 

The  old  custom  of 
to  12  parts  was  oon- 

from  midnight  to 
midnight.  The  day 
rather  than  at  noon 
ilthough  noon  was  of 
id  to  be  determined. 
10  studied  the  annual 
n  quite  evident  that 
e  passages  over  the 

the  next,  could  not 
[)eoau8e  the  apparent 

is  not  ooDfitant.  It 
snt  revolution  of  the 
M  thing,  the  diurnal 
xi8,may  be  regarded 
[pHipomft.  Thisrev- 
uoendon  a»  explained 
If  thesuninoeiied 
aievery  day,  H  would 

day,  as  measured  by 
k  between  suooeisive 

motion  of  the  ion  in 
o causes:  (1)  ttoun- 
aal  resiihition  arouad 
the  orbit,  and  (2)  tlw 


obliquity  of  the  ecliptic.  How  the  first  cause  nroduces  an 
inequality  is  obvious,  and  its  approximate  amount  is  readily 
computed.  We  have  seen  that  the  angular  relodty  of  a 
planet  around  the  sun  is  inversely  as  the  sqnare  of  its  ra- 
dius vector.  Taking  the  distance  of  the  earth  from  the  sun 
as  unity,  and  putting  e  for  the  eccentricity  of  its  orbit,  its 
greatest  distance  about  the  end  of  June  is  1  +  «  =  1  •  0168, 
and  its  least  distance  about  the  end  of  December  is 
1 — 0  •  0168.  The  squares  of  these  quantities  are  1  •  034  and 
1_.034  very  nearly  ;  therefore  the  motion  is  about  one 
thirtieth  greater  than  the  mean  in  December  and  one 
thirtieth  less  in  June.  The  mean  motion  is  3*°  56* ;  the 
actual  motion  therefore  varies  from  3""  48'  to  4"  4'. 

The  effect  of  the  obliquity  of  the  ecliptic  is  still  greater. 
When  the  sun  is  near  the  equinox,  its  motion  along  the 
ecliptic  makes  an  angle  of  23^"  with  the  parallels  of  dec^ 
lination.  Since  its  motion  in  right  ascension  is  reckoned 
along  the  parallel  of  declination,  we  see  that  it  is  equal  to 
the  motion  in  longitude  multiplied  by  the  cosine  of  23^°. 
This  cosine  is  less  than  unity  by  about  ^OT ;  therefore 
at  the  times  of  the  equinox  the  mean  motion  is  diminished 
by  this  fraction,  or  by  20  seconds.  Therefore  the  days 
are  then.  20  seconds  shorter  than  they  would  be  were  there 
no  obliquity.  At  the  solstices  the  opposite  effect  is  pro- 
duced. Here  the  different  meridians  of  right  ascoasion 
are  nearer  togetiier  than  they  are  at  the  equator  in  the 
proportion  of  the  ooaina  of  2S|°  to  unity  ;  ^erefore,  when 
the  sun  moves  through  one  degree  along  the  ecliptic,  it 
changes  its  rig^t  ascension  by  1*08°  ;  here,  therefore,  the 
day*  are  about  19  seconds  longer  than  they  would  be  if  the 
obliquity  of  the  ecliptic  was  zero. 

Wo  thna  have  to  recognize  two  slightly  different  kinds 
of  days :  aciaf  days  and  mtmk  days.  A  solw  day  is  the 
interval  of  time  betweon  two  successive  transits  of  the  sun 
over  the  same  meridian,  while  a  mean  day  is  the  mean  of 
all  the  solar  days  in  a  yea?.  If  we  had  two  docks,  the 
one  going  with  perfect  uniformity,  but  regulated  so  as  to 


260 


A8TR0N0MT. 


keep  M  near  the  sun  as  poBBible,  and  the  other  changiTig 
its  rate  so  as  to  always  follow  the  sun,  the  latter  would  gain 
or  lose  on  the  former  by  amounts  sometimes  rising  to  22 
seconds  in  a  day.  The  accumulation  of  these  variations 
through  a  period  of  several  months  would  lead  to  such 
deviations  that  the  sun-clock  would  be  14  minutes  slower 
than  the  other  during  the  first  half  of  February,  and  16 
minutes  faster  during  the  first  week  in  November.  The 
time-keepers  formerly  used  were  so  imperfect  that  these 
inequalities  in  the  solar  day  were  nearly  lost  in  the  neces- 
sary irregularities  of  the  rate  of  the  clock.  All  clocks 
were  therefore  set  by  the  sun  as  often  as  was  found  neces- 
sary or  convenient.  But  during  the  last  century  it  was 
found  by  astronomers  that  the  use  of  units  of  time  vary- 
ing in  this  way  led  to  much  inconvenience  ;  they  there- 
fore substituted  mean  time  for  solar  or  appcvrent  ^ame. 

Mean  time  is  so  measured  that  the  hours  and  days  shall 
always  be  of  the  same  length,  and  shall,  on  the  average,  be 
as  much  behind  the  sun  as  ahead  of  it.  We  may  imagine 
a  fictitious  or  mean  sun  moving  along  the  equator  at  the 
rate  of  8"  56*  in  right  ascension  every  day.  Mean  time 
will  then  be  measured  by  the  passage  of  this  fictitious  sun 
across  the  meridian.  Apparent  time  was  used  in  ordinary 
life  after  it  was  given  up  by  astronomers,  because  it  was 
very  easy  to  set  a  dock  ftova.  time  to  time  as  the  sun 
passed  a  noon-mark.  But  when  the  dodi  was  so  far  im- 
proved that  it  kept  much  better  time  than  the  sun  did,  it 
was  found  troublesome  to  keep  putting  it  backward  and 
forward,  so  as  to  agree  with  the  sun.  Thus  mean  time 
was  gradually  introduced  for  all  the  purposes  of  ordinary 
life  except  in  vety  remote  country  distriots,  where  the 
farmers  may  find  it  more  troublesome  to  allow  for  an  equa- 
tion of  time  than  to  set  their  docks  by.  the  sun  every  few 
days. 

The  conun<m  household  almanac  should  give  the  equa- 
tion of  time,  or  the  mean  time  at  which  the  sun  passes  the 
meridian,  on  eadi  day  of  the  year.  Then,  if  any  one  wialiM 


tUPBbVlNO  TUB  OALBNDAB, 


^61 


I  the  other  changii  g 

the  latter  would  gain 

ometimes  riaing  to  22 

of  these  variations 

would  lead  to  such 

)e  14  minutes  slower 

of  February,  and  16 

in  November.     The 

imperfect  that  these 

arly  lost  in  the  neoes- 

he  clock.    All  docks 

sn  as  was  found  neces- 

le  last  century  it  was 

f  units  of  time  vary- 

venience  ;  they  there- 

lar  or  appewent  time. 

le  hours  and  days  shall 

hall,  on  the  average,  be 

'  it.     We  may  imagine 

Dg  the  equator  at  the 

<rery  day.     Mean  time 

ge  of  this  fictitiouB  sun 

le  was  used  in  ordinary 

lomers,  because  it  was 

ne  to  time  as  the  sun 

le  dock  was  so  far  im- 

ae  than  the  Mm  did,  it 

ittingit  backward  and 

(un.    Thus  mean  time 

B  purposes  of  ordinary 

ry  districts,  where  the 

ne  to  allow  for  an  equa- 

I  by.  the  sun  every  few 

I  should  give  the  equa- 
rhich  the  ran  passes  the 
Then,  if  any  one  wiakM 


to  set  his  clock,  he  knows  the  moment  of  the  sun  passing 
the  meridian,  or  being  at  some  noon-mark,  and  sets  his 
time-piece  accordingly.  For  all  purposes  where  accurate 
time  is  required,  recourse  must  be  had  to  astronomical  ob- 
servation. It  is  now  customary  to  send  time-signals  every 
day  at  noon,  or  some  other  hour  agreed  upon,  from  obser- 
vatories along  the  principal  lines  of  telegraph.  Thus  at 
the  present  time  the  moment  of  Washington  noon  is  sig- 
nalled to  New  York,  and  over  the  principal  lines  of  rail- 
way to  the  South  and  West.  Each  person  within  reach  of 
a  telegraph-office  can  then  determine  his  local  time  by  cor- 
recting these  signals  for  the  difference  of  longitude. 

8  4.    RmffARTTB  ON  DCPBOVma  THE  OAXMSDAIL 

It  is  an  interesting  question  whether  our  calendar,  this 
product  of  the  growth  of  ages,  which  we  have  so  rapidly 
described,  would  admit  of  decide<l  improvement  if  we 
were  free  to  make  a  new  one  with  cae  improved  nuiterials 
of  modem  science.  This  question  i»  not  to  be  hastily  an- 
swered in  the  affirmative.  Two  small  improvembPte  are 
undoubtedly  practicable  :  (1)  a  more  regular  divisicn  of 
the  866  days  among  the  months,  giving  February  80  diiys, 
and  so  having  months  of  80  and  81  days  only  ;  (2)  putting 
the  additional  day  of  leap  year  at  the  end  of  the  year  in- 
stead of  at  the  end  of  February.  The  smallest  change 
Afom  oui  ^iresentoystem  wonld  be  made  by  taking  the  two 
additional  days  ic»  February,  the  ooe  from  the  erd  of 
July,  and  theotL  <v  ,*rom  the  end  of  December,  leaving 
thelait  wlb  30^&,'i  in  rommoa  yean  and  31  in  leap 
yeats.  When  wp  c-o;  i  Jder  more  radical  changes  thnn  this, 
we  find  advaiihges  set  off  by  disadvantages.  For  in- 
stance, it  WA^td  on  some  ^yonuts  be  very  ocHimikient  to 
divide  th6  /t-^  into  18  monUtf.  of  4  weelm  each,  the  last 
month  liavinf  one  or  two  extra  (kys.  The  months  wonld 
then  begin  cm  the  aanie  day  of  she  week  throi^  oaeh 
year,  ai^  woidd  admit  of  a  luuoh  moie  oonvwoient  aabdi- 


Mi 


ASTHONOMT. 


\   1 


vision  into  halves  and  qnarters  than  tliey  do  now.  But  the 
year  would  not  admit  of  snch  a  subdivision  without  divid- 
ing the  months  also,  and  it  is  powible  that  this  inconven- 
ience would  balaDce  the  conveniences  of  the  plan. 

An  actual  attempt  in  modern  times  to  form  an  entirely 
new  calendar  is  of  sufficient  historic  interest  to  be  men- 
tioned in  this  connection.  We  refer  to  the  so-called  Bepub- 
lioan  Oalendar  of  revolutionary  France.  The  year  some- 
times had  365  and  sometimes  366  days,  but  instead  of 
having  the  leap  years  at  defined  intervals,  one  was  inserted 
whenever  it  might  be  necessary  to  make  the  autumnal 
equinox  fall  on  tlie  first  day  of  the  year.  The  division  of 
the  year  was  effected  after  the  plan  of  the  ancient  Egyp- 
tians, there  being  12  months  of  30  days  each,  followed  by 
5  or  6  supplementary  days  to  complete  the  year,  which 
were  kept  as  feast-days.*  The  sixth  day  of  course  occur- 
red only  in  the  leap  years,  or  J^emciads  as  they  were  call- 
ed. It  was  called  the  Day  of  the  Bevolution,  and  was  set 
apart  for  a  quadrennial  oath  to  remain  free  or  die. 

No  attempt  was  made  to  fit  the  new  calendar  to  the  old 
one,  or  to  render  the  change  natural  or  o-onvenient.  The 
year  began  with  the  autumnal  equinox,  or  September  22d 
of  the  Gregorian  calendar ;  entirely  new  names  were 
given  to  the  months  ;  the  week  was  abolished,  and  in  lieu 
of  it  the  month  was  divided  into  three  decades,  the  last  or 
tenth  day  of  each  decade  being  a  holiday  set  apart  for  the 
adoration  of  some  sentiment.  Even  the  division  of  the  dar 
into  24  honrs  whs  done  away  with,  and  a  division  into 
ten  hours  was  substituted. 

The  Republican  Cfdendar  was  formed  in  '  7')8,  the  year 
1  commencing  on  September  22d,  119:^,  and  it  was 
abolished  on  January  1st,  1806,  after  13  years  of  con- 
fusion. 

*  Hi^  reeeived  the  niduumw  of  »an»-euk4IUlt$,  from  the  oppoMOti 
(rf  the  new  etato  of  thlaga. 


ey  do  now.  But  the 
ivision  without  divid- 
e  that  this  inconven- 
}  of  the  pUm. 
8  to  fonn  an  entirely 
interest  to  be  men- 

0  the  80-called  Bepnb- 
ice.  The  year  some- 
days,  but  instead  of 
rvals,  one  was  inserted 

make  the  autumnal 
ear.  The  division  of 
of  the  ancient  Egyp- 
ays  each,  followed  by 
)lete  the  year,  which 

1  day  of  couTM  occur- 
iads  as  they  were  call- 
evolution,  and  was  set 
iu  free  or  die. 

ew  calendar  to  the  old 
1  or  convenient.  The 
tox,  or  September  22d 
ely  new  names  were 
i  abolished,  and  in  lieu 
■ee  decades,  the  last  or 
>liday  set  apart  for  the 
1  the  division  of  the  dar 
1,  and  a  division  into 

rmed  in  '  r')8,  the  year 
Id,  l'<92,  and  it  was 
kfter  13  years  of  con- 


kUUm,  ftam  die  opponento 


THE  ABTRONOMJOAL  EPHSMBSIS. 


263 


$i  6.    THE  ABTBONOMiaAL  SPHXICEBIB,  OB  NAU- 
TIGAIi  ALMAirAO. 

The  Aatronomvcal  EpJiemeris,  or,  as  it  id  more  com- 
monly called,  the  UTaviical  Almanac,  is  a  work  in  whicli 
celestid  jAenomena  and  the  positions  of  the  heavenly 
bodies  are  computed  in  advance.  The  need  of  snch  a  work 
mnst  have  been  felt  by  navigat.rs  a^id  astronomers  from 
the  time  that  astronomical  predictions  became  eofficicutly 
accurate  to  enable  them  to  determine  their  position  on  the 
surface  of  the  earth.  At  first  works  of  this  class  were  pre- 
pared and  published  by  individual  astronomers  who  had 
the  taste  and  leisure  for  this  kind  of  labor.  Manfredi, 
of  Bonn,  published  Ephemeride9  in  two  volumes,  which 
gave  the  principal  aspects  of  the  heavens,  the  positions  of 
the  stars,  planets,  etc.,  from  1715  nntil  1725.  This  work 
included  maps  of  the  civilized  world,  showing  the  paths  of 
the  principal  eclipses  during  this  interval. 

^e  usefulnem  of  such  a' work,  especially  to  the  naviga- 
tor, depends  upon  its  regular  appearance  on  a  uniform  plan 
and  upon  the  fiilness  and  accuracy  of  its  data ;  it  was  there- 
fore necessary  that  its  issue  should  be  taken  up  as  a  gov- 
ernment work.  Of  works  of  this  class  still  issued  the 
«arlie8t  was  the  ConnaiMmuse  dea  Ternps  of  France,  the 
first  volume  of  which  was  published  by  Picabd  in  1679, 
and  which  has  been  continued  witilout  interruption  until 
the  present  time.  The  publication  of  the  British  Na^Moci 
.AlmamiiC  was  commenced  in  the  year  1767  on  the  repre- 
sentations of  the  Astronomer  Soyal  showing  that  such  a 
work  would  enable  the  navigator  to  determine  his  longi- 
tude witiiin  one  degree  by  observations  of  the  mo<m.  An 
astronomical  or  nautical  almuiao  is  now  published  annually 
by  each  of  the  governments  of  Germany,  Spain,  Portugal, 
Fnuuw,  Ghreat  Biitein,  and  the  dnited  States.  They  have 
gradnatty  inereMed  in  size  and  eitent  with  the  advancing 
waotaW  tiie  artrmunner  until  those  of  Great  Britain  and 
this  oQfontry  have  become  ootovo  vohiinee  of  between  500 


264 


ABTRONOltT. 


and  600  pages.  These  two  are  published  three  yean  or 
more  beforehand,  in  order  that  navigators  going  on  long 
voyages  may  supply  themselves  in  advance.  The  Ameri- 
can Ephsmeris  and  Nautical  Almanac  has  been  regular- 
ly published  since  1855,  the  first  volume  being  for  that 
year.  It  is  designed  for  the  use  of  navigators  the  world 
over,  and  the  greater  part  of  it  is  especially  arranged  for 
the  use  of  astronomers  in  the  United  States. 

The  immediate  object  of  publications  of  this  class  is  to 
enable  the  wayfarer  and  traveller  upon  land  and  the  voy- 
ager upon  the  ocean  to  determine  their  positions  by  obser- 
vations of  the  heavenly  br  "^ies.  Astronomical  instruments 
and  methods  of  calculation  have  been  brought  to  such  a 
degree  of  perfection  that  an  astronomer,  armed  with  a  nau- 
tical almaiiac,  n  chronometer  regulated  to  Greenwich  or 
Washington  time,  a  catalogue  of  stars,  and  the  necessary 
instruments  of  observation,  cai>  determine  his  position  at 
any  point  on  the  earth's  surface  within  a  hundred  yards 
by  a  single  night's  observations.  If  his  chronometer  is 
not  so  r^ulated,  he  can  stUl  determine  his  latitude,  but  not 
his  longitude.  He  could,  however,  obtain  a  rough  idea 
of  the  latter  by  observations  upon  the  planets,  and  oome 
within  a  very  few  miles  of  it  by  a  single  observation  on 
the  moon. 

The  Ephemeris  furnishes  the  fundamental  data  from 
which  all  our  household  almanacs  are  calculated. 


The  principal  quantities  given  in  the  Amniiam  Rphemeri*  for 
eaflb  year  we  as  follows  ; 

The  poeitiont  of  the  sua  and  the  principal  large  i^aaete  for  Qmn' 
wich  noon  of  every  oay  in  each  year. 

'tha  right  aaceaiiiitt  and  aeoiiniition  of  the  nioon*s  eentn  far 
evwy  hmtr  in  UN  year. 

The  dietaam  of  ^he  moon  from  certain  bright  itan  aad  pliwli 
for  everv  thira  hour  of  the  year. 

The  niriiteaaeaaions  and  aeciinationsof  upward  of  two  hundrad 

^  the  bdigliler  fixed  etan,  corrected  for  pteoeieion,  ntttertcw,  aad 


abemtfoiL  for  eveiy  ten  dnrs. 
TlMMUtioMOf  fbe  principal  plWMts  at  every  visible  trai^t  over 

Oonplete  iliwiiitii  oTaU  tha  aoUpies  of  tbe  mm  iad  wooii,  with 


)li8hed  three  yean  or 
igators  going  on  long 
dvance.  The  Ameri- 
mae  has  been  regnlar- 
rolume  being  for  that 
f  navigators  the  world 
especiidly  arranged  for 
d  States. 

lions  of  this  class  is  to 
pon  land  and  the  voy- 
leir  positions  by  obser- 
tronomical  instmments 
een  brought  to  such  a 
ner,  armed  with  a  nan- 
ated  to  Greenwich  or 
ars,  and  the  necessary 
termine  his  position  at 
ithin  a  hundred  yards 
If  his  chronometer  is 
line  his  latitude,  but  not 
r,  obtain  a  rough  idea 
ijie  planets,  and  oome 
single  observation  on 

'nndamental  data  from 
ire  calonkted. 

t  AmniioHi  Fphemerto  for 

psllMgairiMMto  for  anrap 

of  the  mooB's  eotn  for 

B  bright  atut  sad  plMMli 

at  upwud  of  two  ItOBdrad 
»  pteoearion,  nntallaii,  and 

tA  erery  vUibU  traiytt  ovsr 

of  fli0  nw  iDfl  mooiii  iHth 


TITS  BPHBMBRja. 


265 


maps  showing  tho  passage  of  the  moon's  shadow  or  penumbra  over 
those  regions  of  the  earth  where  the  eclipses  will  be  visible,  and 
tables  whereby  the  phases  of  the  eclipses  can  be  accurately  com- 
puted for  any  place. 

Tables  for  predicting  the  occultations  of  stars  by  the  moon. 

Eclipses  of  Jupiter'' I  satellites  and  miscellaneous  phenomena. 

To  give  the  reader  a  still  further  idea  of  the  Bphemerit^  we  pre* 
sent  a  small  portion  of  one  of  its  pages  for  the  year  1888 : 

Fbbroart,  1888^at  Qrbbnwich  Mban  Nooif. 


week. 

Tn  Sim 

'• 

BqnaUoa 

orUmeto 

beub- 

traeted 

time. 

i 

i 

Sh 

Of 
M 

n 

lereiUUma 

AppMent 

rlghlMeeB- 

■lon. 

Diff. 
fori 
boar. 

ipperentde- 
Uiwitlou. 

Die 
fori 
how. 

rMitaa- 
niSonof 

ICUMUI. 

Wed. 
Tbnr. 
Frid. 

Sl 

n 

m. 
0 
4 
8 

1. 
18-04 
K-84 
19-a 

■. 

w-m 

10-141 

lo-ior 

• 

817 

16 

16 

9 

45 
87 

■ 

a-4 

6-4 

a-9 

• 

44-a 

a-     ■. 

U    61-84 
18    W-U 
14     6-01 

1. 

0-818 
0-984 
OIW 

a. 

a 
a 
a 

v.       •. 

a  n-m 
a  u-a 

64    14-M 

Mm. 

M 

n 

19 
16 

a 

91-a 
aa 
a-a 

10  on 

1O-O40 
10-087 

18 
16 
16 

9 
M 

a 

a-9 
a-8 

8-1 

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Tea 

a-a 

14    10-81 
14    16-41 
14    19-a 

0-918 

oia 

0-lW 

a 

91 
91 

a  11 -a 
9  7a 
8    4-a 

Thw. 

n 
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n 

94 

a 
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t-Nl 
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ts  67-a 
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40 
44 

1S:S 

lo-a 

9-877 
9-8a 
9-816 

14 

tt 

a 

18 

or 

87 

61-8 
11-9 

a-9 

a-47 
a-a 

.14  a-61 
14  r-a 
14  a-a 

o-ao 

0-011 

o-oa 

91 

n 
n 

91  a-a 

a  47-a 
a  ua 

Kba. 
Tms. 
Wed. 

18 
14 
IS 

tl 
91 

a 
a 
a 

S:8 

64-M 

9-784 
9-ia 
9-TB 

u 

19 

a 

IT 

a 

a 

9-1 

a-8 

14-9 

4w.a 
61-n 
61  a 

14  aa 
14  aa 
14  a-a 

0-184 

a 
a 
a 

a  aa 

M 
17 
M 

a 

a 

8 

7 

4717 
88^ 
81 -a 

9-8a 
9-8M 

9-8a 

18 

It 
11 

IS 
64 

a 

a-8 

ai 
a-8 

-H»l4 
Ti-a 

14    1MB 

14  19-a 

14     T-N 

0184 

o>ia 
o>9a 

M 

SS:S 

a  a-ii 

Of  the  same  general  nature  with  the  Sphemeris  an  catalogues  of 
the  fix  >d  stars.  The  ol^Jaet  <rf  such  a  oanlogue  is  to  give  the  rj|riM 
aaeaiuioB  and  deelinstioa^  a  nomber  of  atars  far  soate  epock,^a 
b^gnuBing  of  the  year  1875  for  isitaiice,  with  Ha  data  by  wMA  tl» 
nodtion  of  a  star  can  be  fauid  at  aay  other  opoch.  awh  oalih 
logoaa  ar&  however,  imperfeet  owing  to  the  cwwutant  naall  nhaaiia 
in  the  poatlonsfrf  tito  aara  and  the  enon  aw^  iuaerl^eMoM  ofwa 
older  ooaervations.  In  conaequMwe  of  theae  taapernoaiMs,  a  oomM- 
eraUe  part  of  the  work  of  the  astronomer  eagaMd  %k  accurate  d»> 
tanfautioiu  of  geoaraphioal  poaltioas  oomfaitlk  8m^  tfew  i 
aoeunt«  poaittsBS  oFtta  atara  which  he  aaka  -mi  oi. 


h 


PART   II. 

THE  SOLAR  SYSTEM  IN  DETAIL 


CHAPTER  I. 
STRUCTURE  OF  THE  SOLAR   SYSTEM. 

Thb  solar  system,  as  it  is  known  to  ns  through  the  dia- 
ooveries  of  Copebnious,  Kepleb,  Newton  and  their  sue- 
oeasors,  consists  of  the  sun  as  a  central  body,  around  which 
revolve  the  major  and  minor  planets,  with  their  satellites, 
a  few  periodic  comets,  and  an  unknown  number  of  meteor 
swarms.  These  are  permanent  members  of  the  system. 
At  times  other  comets  appear,  and  move  usually  in  par- 
abolas through  the  system,  around  the  sun,  and  away  from 
it  into  space  again,  thus  visiting  the  system  without  be- 
ing permanent  members  of  it. 

The  bodies  of  the  system  may  be  classified  as  follows  : 

1.  The  odntnil  body —the  Sun. 

2.  The  four  inner  planets— Jferottry,  VentUy  the  fourth, 
Mw. 

8.  A  group  of  pmall  planets,  sometimes  dSkA  AKteroidi^ 
revolving  outside  of  the  orMt  of  Mara. 

4.  A  group  of  fcwr,  outer  planets — J-upitett  Saturn, 
Urtmm^  KadJ^tpinme. 

6.  The  MitenitflS,  or  secondary  bodies,  revolving  about 
Urn  piMMli,  mMat  primaries. 

ft,  A  number  of  comets  and  meteor  swarms  revolving 
in  ^pfy  eooenlric  orbits  about  the  Sun. 


jjgg  ABTRONOMT. 

by  Sir  Wil  ..taL  Hi^hboukl  in  1802,  are  worihy  of  repe- 
*'*'^et.  are  celestial  bodies  of  a  certain  very  conaider- 
''"Th^'move  in  not  very  eccentric  ellij-ea  abont  the 

'"^The  pUnea  of  their  orbita  do  not  deviate  many  degreea 
from  the  plane  of  the  earth',  orbit.  ^^ 

Their  motion  abont  the  ann  ia  direct.  1^ 

mm,  Umb^  how  far  thb  in»y  1»  "»*«  to  y«t  »» 

*^  „,«  to  v«7  »»»««  elMp»  "  "- P-"^ 
-^i^:j:i«b  motion  .*nll,rf  ihep-i-t  «<.*r 

'"SlfS::  of  **«»*- i.  *» '"-^ -"^ 
alt; 


md  4  are  BometimeB 
I,  to  distinguiBh  them 
,r  jdaneUt  oi  Gronf  9. 
)nB  claaaefl,  laid  down 
J,  are  worthy  of  repe- 

certain  very  conaider- 

tric  ellip«»  about  the 

deviate  maiiy  degreea 

rect. 

B. 

ideiable  extent,  which, 
)le  proportion  to  their 

iderable  dirtanoea  from 

y  known  as  mmU  w 
which  move  about  the 

of  oonaiderable  eooen- 
may  be  inclined  to  the 

They  may  or  may  not 

be  Mmtoed  ia  y«k   un- 

eliipaea  or  in  paraboHo 

n^of  thegreatatt  v«riety 

a  i»  dao  totaBy  «id||ir- 

ny jpwit  exMoW***** 


Th«  nillttt  afpwrai  n^  ihe  shn,  as  leen 

from  ^  ^Moai  i^lMiet8»  is  ahdWA^i  the  next  figure. 

JPfard  and  JffMMMyiM  an  two  of  tiM  asteroids. 

A  oiirioiswlilfcm  between  the  disfeHMes  of  the  planets, 
known  is  Bani^lMr,denmsmentkNi.    IftoAennm- 

bers, 

O,8,0,1%«A,48,»«»1M,884, 


^M-. 


870 


ASTROlfOMT. 


eaoh  of  which  (the  tiocond  exorptod)  ib  twioo  the  prooed- 
ing,  wo  add  4,  we  obtain  the  Berics, 

4,  7,  10,  16,  28,  52,  100,  106,  888. 

Those  last  numbers  represent  approji  i  itely  {\w  dia- 


Fie.  76.— ijrrAauTT  UMiKxtnam  or 

vnurr 


vn  MM 


rmm  Mr> 


tonoes  of  tiie  pluietB  from  tiie  am  (exoept  for  JffplmMf 
which  was  not  disoovered  whm  the  ao-oalled  bw  was  an- 
nonnoed). 
Thia  ia  ahown  in  the  following  table : 


-■«%^\-V--,*^j<::^-^^,^.:^i^-;ff.^!l.'£-^<^ifrgr^' 


is  twice 


,  106,  888. 

pproA  .1  >tely  tlm  dia- 


an  (except  for  Ntfti^uMf 
to  80-called  law  waa  «a- 

teble: 


IMAGE  EVALUATION 
TEST  TARGET  (MT-3) 


4f 


1.0  ^tma 

Itt  122  a  2.2 
lu  — 

u 

Itt    12.0 


CIHM/ICMH 


Series. 


CIHM/ICMH 
Collection  de 
microfiches. 


Camdiwi  liwdtuM  lor  HiMorieal  Mlcroftproductloiit  /  InMNut  caMcHwi  <(•  nrtcroreproductlOM  Muoriqim 


0HABACTERT8TI08  OF  THE  PLANETS. 


871 


PLAinm. 


Mereary 
Venas. . 
Earth. . . 
Man . . . 
rCerai]. . 
Jupiter . 
Saturn.. 
Uranus. . 
Neptune 


Antul 

Distance. 

Bode't  Law. 

8-9 

40 

73 

70 

100 

100 

15-3 

160 

87-7 

380 

03  0 

08-0 

9S-4 

100.0 

191-8 

106-0 

800-4 

8880 

It  will  be  observed  that  Neplnme  does  not  fall  witiiin 
this  ingenioos  scheme.    Cere»  is  one  of  the  minor  planets. 

The  relative  brightness  of  the  sun  and  the  various 
planets  has  been  measured  by  Zoixnbr,  and  the  results 
are  given  below.  The  column  -per  oent  shows  the  per- 
centage of  error  indicated  in  the  separate  reanlts : 


Suit  Axn 

Bitlo:lto 

PucantorBmr. 

Moon 

618,000 

6,99i000i«» 

5,479,000,000 

180J80,OdO,000 

8,488,000,000.000 

lo^no.ooo/100,000 

1>6 

Man 

6-8 

Jupiter 

6-7 

Batam  (ball  alone) 

Urmwi i 

60 
6*0 

Neptnne...... 

5>5 

The  d^OnooM  in  ihe  dm^ty,  aiae,  mam  and  distance 
of  the  aoiiillilltiieti^  and  ih  the  amoani  fA,  aokr  li^t 
and  heafe  viliii  titej  ■•nowiv,'  are  immonae.  IPie  diatmoe 
of  Neplm0^li:nil^^isam  libtit  of  JfaroMy,  and  it  re- 
ceivw  <n3i^t4i%  m  aoaoh  I^i^  and  heat  fimm  the  aim. 
The  detiril]^  tH  the  earth  !■  abofvt  aSx  timea  tiwt  of  ?Mlor, 
whOe  Saimi?i  moan  ^bmmtbj  ia  la*  than  tfaft  of  urattr. 

Hm  maoa  <lf  the  ann  ia  iu  graater  than  that  olaii|f 

alng^  |l«Mt  in  tiie  ayslflitt,  or  indeod  than  the  oonOiiBted 

pumidt&^ikBm.    !bi  gip«nkl)itia  it  rNnarfcaMe  fact 

,  thiA  the  nam  of  any  giT«n  phmrt  eaBoeeda  tiie  anm  of  the 

■mtmu  of  aH  the  phaeta  of  laai  mm  tibaa  itielf.    Thfiila 


-.-/■'^.-.-.T.-.j.Ttifrri^r'^ 


272  A8TB0N0MT. 

Bhown  in  the  followingtable  where  the  ma«^  of  th^^ 
ets  are  taken  as  fractions  of  the  sun's  maw,  which  we  here 
express  as  1,000,000,000: 


I 


a 


1" 


i 


SM    l;»8   8,000    44^ 


I 


i 


Bi.aoo  «5;i8o.  w4,aoB 


& 


Pi^Mm. 


1,000,000,000    Mmm*. 


MO  < 

634  < 
»,8Ty  < 
5,087  < 

80,187  < 


884 

8,858 
8.080 

too 

81.800 
886,580 
864;806 


The  nuw  of  Mercuty  ta  te«  tlwn  the  maw) 
of  Man:  > 

The  samof  OMwesof  Mercury  and  Mare) 
is  leaa  than  the  man  of  Yenoa :  ) 

Mercury  +  Mars  +  Venus  <  Earth: 
Merwuy  +  Mars  +  Venus  +  Bwth  <  Um- ) 

nus:  ' 

Mereury  +  Mars  +  Venaa  +  Barth  +  Ura-) 

BUS  <  Neptune :  > 

Meieurr  +  Mars  +  Venus  +  Earth +  Ura- J     tOl.787  < 

una  +  Neptune  <  Batnm  :  ) 

Meieuiy  +  Mara  +  V«ins  +  »«*+J?l»-|    887,887  < 
iSi  + Neptune  +  Saturn  <J«plter:     J 

ComMaed  mass  of  all  the  plaaeta  ialess)  |^«n  <;  ififM^fiMfiM 
tlMA  that  of  the  San:  i 

The  total  mass  of  the  smaK  phneti,  like  ^^^J^^^ 

of  ^  aboT*  nu-et  of  Hie  lokr  |y^  by  """^^ T* 
or  two  units.  The  -un's  m«8  i-  *b»  oi»r  700  time,  thrt 
of  r&e  o&er  bodie.,  «id  him« tto  f^ of  iti ««.^ 
poritioa  in  the  soUir  •y»tf\  *•  f**^  ^^^ 

oatiide  the  body  of  the  Mm,  and  will  be  taild^^  J'*'*** 
/«mtor  and  .8Wim»  are  in  opiporfto  difjejo^^ 

the  aim  have  been  expWnrf  to  »aSL^J^J2 
i.  there  said  it  .ppewB  tin*  the  b«t  tl«ete»#«i»  ««  «« 


PLANET  ART  ABPBGTB. 


373 


B  masses  of  the  plan- 
aass,  which  we  here 


PiiAifvn. 

4.806 

1.000,000,000 

MaMM. 

900  < 

8» 

1 

outer  planets  will  be  when  it  is  in  opposition— that  is,  when 
its  geocentric  longitude  or  its  right  ascension  differs  180° 
or  12^  from  tbat  of  the  sun.  At  such  a  time  the  planet 
will  rise  at  sunset  and  culminate  at  midnight.  During  the 
three  months  following  opposition,  the  planet  will  rise  from 
three  to  six  minutes  earlier  every  day,  so  that,  knowing 
when  a  planet  is  in  opposition,  it  is  easy  to  find  it  at  any 
other  time.    For  example,  a  month  dfter  opposition  the 


684  < 

»m 

%m  < 

<.0«0 

mt  < 

Imw 

80,187  < 
101,787  < 


vfim  < 


51,000 


tMMiOO 


tlMjM» 


ts,  like  their  number, 
than  one  ttwuMidth 
iaanma^mm  idtal 
kem  by  wa^^km  one 
iw  o^  700  tfmes  that 
tthe  faekof  Uieentnkl 
c|laiiied.    In  lMt,i)w 
IV  Mwfeem  it  ^^1^9^  liktie 
mbeiniidealitwbifi 
diraetloMfroaiit 
M  of  43w  ^taaoli  libmit 
iplwIT.    Fremwbift 
I  tteeto«M)  ^MM  ef  tte 


fkn^mB^htimoUi  4iim  boars  bi|^  abont  miiiMl,and 
wIlL  enlninitoidMil  nfaie  or  tea  o'elodk.  ^Of  oowie  the 
hwwr  pi Witti  aoiit  eoaw  ^ito  q>pQsition,  and  benee  are 
bMl  Mm  abiMt  Ibe  t&Mt  of  tbeir  gieeutest  elqiigetioiw. 
^  «bofe  Ignv  ^PM  ft  roai^  fSm  of  pact  ^  tbe 

lyitiuft  m^imoHmpf^  to  ft^^eetator  immr^ieHjy 

t  or  MOW' Jie  fii«*ol  Ibe  ed!]^ 


874 


ABTBOirOMT. 


It  is  drawn  approximately  to  scale,  the  mean  distance  of 
thee«rth(=l)  being  half  an  inch.  The  mean  diatMice  of 
Sa^tm  would  be  4-77  inches,  of  Uranwt  OoD  inches,  of 
Nep^tme  1503  inches.  On-the  same  scale  the  distance  of 
the  nearest  fixed  star  wonld  be  103,133  inches,  or  over  one 
and  one  half  miles.  . 

The  arrangement  of  the  planets  and  satellites  is  then— 

«  AatamUa  The  Oatw  OcMqk 

TheliuwrOfoop.  Aiteronn.  /  Jupiter  and  4  moon*. 

Mercaiy.  )    aoo  minor  pUaeU.  \  htam  Mi  SaMona 

VewM.  \      ud   probably  <  Unuiu  ■■«  4  pwaa. 

Earia  ma  Mom.         i        maar  mon.  f  Waniaaa  aad  liMaoa. 

BlanaiitWMMM.      J        ^^  ^  »ap«ma aw » -ip" 

To  awid  lepetitiona,  the  elements  Of  ihe  major  plwets 
and  o«lier  data  are  ooUeotod  into  the  two  foUowtog  ««Wtt», 
towhidi  iwfaence  may  be  made  by  the  atudwit.  _The 
unite  in  terms  of  which  the  varioua  ^nantitwa  «•  fiten 
arelhow  familiar  to  m,  ■•  mileB,  daya,  etc,  y«fc  Jon»  of 
the  dklMwea,  etc,  aw  ao  immenwily  greater  tbio  any 

lounm  to  our  dafly  experience  that  we  muat  I*''  »««"* 
to  ffl-trationa  to  obtdn  «y  id«t  rf  ^  at  JL    F«rex- 

annle.the  dJataaoeol  the  aoniaMd  tobeW*  «««»» 
3^^  It  i.  of  i«pert«ce  tM  eoB*  idea  d«mM^ 
of  tliitdistaiifle,ie  it  it  the  unit,  in  tenM  of  wMA  Jot 

on^  flie  cHrtMH*.  in  the  '^'^S^  S^.S^'Html 
w^  i«v«a  aa  a  b«ib  for  nwatuaeia  tkeetcfiur  vttNtw. 

tST^  we ..y  that  th^«lt-«  2.^ 

.90%M»  tbnea  tbe  hmhi  dlrtttice  «f  ^'«?«  .^>  y^^ 

^Z^a»,  to  M  if  aen»  eoMifMo»  fltii  beditaiMM  «>» 
SS^thic  Of  *•  rtlitiiit  i«i*^ 
STnTconoeption.  »fc  ftar  too  g«at  f «r  w  to  We 
counted.  We  have  never  taken  in  at  one  vtow,  ejren 
,  niinion  Bimihr  di«»ete  objects.  To  "onntftwrn  1^ 
900  leqnirw,  with  veiy  rapid  counting,  «0«eeoiidf.  BJ* 
pose^  kept  up  for  ♦  day  without  i"*««^«  v**  ^ 
Uwe  ihouM  have  eennted  288,000,  wM«^  ^/f^,^ 

of  W.6eO,000.      Henoe  over  10  f'«^,^"^°3f^ 

«^  hy  ni^t  and  dg  i«-ddbe  ^ 

^^  ,ll»eiM«i*r,«dkingbBlwet»ie^««*w^ 


EXTENT  OF  TUB  SOLAR  SYSTEM. 


376 


;hemean  distance  of 
l^he  mean  distance  of 
nm  9-i9  inches,  of 
scale  the  distance  of 
(3  inches,  or  over  one 

id  satellites  is  then — 

The  Oatw  OfMp. 

!  Jupiter  and  4  mooiM. 
ftalam  m4  SaMont. 
Naptiuw  Md  1  ■won. 
of  the  major  planets 
two  following  taldes, 
f  the  ila^ait.    The 
qiiantitk»  fro  #ven 
ya,  etc,  ytfc  •orae  of 
Aj  groater  thtn  any 
ra  mnat  haTV^nHNnrse 
them  at  all.    lor  ex- 
id  to  be  09^  mUlion 
a  idM  ahooMVt  luid 
i  termaof  wUili&ot 
ni  are  wpmmAf  but 
la  tfaaateUar  obiVBe. 
I  of  tiM  alMi  il  «ver 
f  theano,  it  bpwmm 
eanbeobfeiilMi^one 
illkb«»»M«M%we 
great  f or  ns  to  nave 
in  at  one  view,  wma 
yTo  eomit  iKNO^  1  ^ 
ting,  flOaeeoBuli^    Bo^ 
I  iiitenaiMtoa;  M  tin 
)0,  wMcli  io  dMiitvb 


the  task  all  idea  of  it  would  have  vanished.  We  may  take 
other  and  perhaps  more  striking  examples.  We  know, 
for  instance,  that  the  time  of  the  fastest  express-trains  be- 
tween New  York  and  Chicago,  which  average  40  miles  per 
hour,  is  about  a  day.  Suppose  such  a  train  to  start  for 
the  sun  and  to  continue  running  at  this  rapid  rate.  It 
would  take  868  years  for  the  joumej.  Three  hundred 
and  sixty-three  years  ago  there  was  not  a  European  settle- 
ment in  America. 

A  caimon-ball  moving  continuously  across  the  interven- 
ing space  at  its  highest  speed  would  require  about  nine 
yearn  to  reaeh  the  sun.  The  report  of  the  cannon,  if  it 
could  be  conveyed  to  the  sun  with  the  velocity  of  sound  in 
air,  would  arrive  there  five  years  after  the  projectile. 
Such  a  distance  is  entirely  inconceivable,  and  yet  it  is 
only  a  small  fraction  of  those  with  which  astivnomy  has  to 
deal,  even  in  our  own  system.  The  distance  of  ITeji^mne 
is  80  times  as  great 

If  we  examine  the  dimensions  of  the  various  orbs,  we  meet 
almost  equally  inconceivable  numbers.  The  diameter 
of  the  son  is  800,000  miles  ;  its  radius  is  but  480,000,  and 
yet  this  is  nearly  twice  the  mean  distance  of  tiie  moon 
from  the  earth.  Try  to  oonodve,  in  looking  at  the  moon 
in  a  clear  sky,  tlu^  i£  the  centre  of  the  sun  oould  be 
placed  at  the  eeiitra  of  the  earlJi,  the  moon  would  be  far 
within  the  raa'a  aorface.  Or^^jain,  omioeive  of  the  f<mie 
of  gmvity  at  the  mrlioe  of  the  vaiioua  bodies  of  the  ays- 
tras.  At tibtf  aui it i| neaily  S8  times  tbatjknown  tons. 
A  pendidant  beating  seeondi  here  would,  if  tiwi8p<nfted 
to  the  sim,  viinwte  witii  a  motion  more  ra]Hd  than  HuA  of 
a  watoh'bdanee.  The  muacleB  of  the  strongest  man  would 
nibk  tttfpiai  tdm  ereet  m  tibe  aurfaoe  o|  &»  ami :  evto 
lying  damn  he  would  erash  himfelf  to  dei^  uncter  his 
oiHl  Wfight  of  two  ton*.  We  n«y  by  these  illnstvatiens 
gttiiHM10i(jph  Idea  of  the  meaning  erf  the  numbers  in 
litm$^i^i^iiii0uiit^  ^  Jae^afcOity  of  our  Hmited  Jdeaa  to 
wm^iat9tmAik»tin^  el  even  I3ie  sohar  qntem. 


S76 


ABTBONOMT. 


■a    58    «5    S    9    »9    9    - 

^S    BB    95    •    S    8^    S    8 

•8  Si  **  8_J_r^_?_I_ 


8  8   88   :s  *- 

9  s  ss  e  8 


$    to    88    8    ^ 

<»    4)    88    8   S 
S    S    88    9    9 


«    S9    5551    8    8    88    9    S 

-  S6  aa  s  «  •"  8  • 

e   88   gj   g   ^   88   g   9 


iliiil 

ni""iroiiT| 


8    f^*-    ^e 


itt 


I 


a  as?  9  * 
s  S9  s  s 

e»     ae     «     •? 

8  88  ?:  *• 
S    SS    !S    8 

to    S8    8    ^ 

9  88    8   S 
S    88    9    9 

^     me*     o     !■* 
et     lOflO.   ►•     y* 

8    88    9    S 
S    •"    8    • 

?3   88   g   9 

3    8g 


II III  I 

msTi 


CHAPTER  II. 

THE    BUN. 


«  1. 

To  the  rtudent  of  the  preBent  time,  armed  with  the 
powerful  meani.  of  research  devised  by  modem  science, 
Sie  sun  presents  phenomena  of  a  very  varied  and  complex 
character.  To  enable  the  nature  of  these  phenomena  to  be 
dearly  underetood,  we  preface  our  account  of  the  physical 
constitution  of  the  sun  by  a  brief  summary  of  the  mam 
features  seen  in  connection  with  that  body. 

FhotaMplMre.— To  the  simple  vision  the  sun  presents 
the  aspect  of  a  brilliant  sphere.  The  visible  sWning  sur- 
face ofthis  sphere  is  called  the  photosphere,  to  distinguish 
it  from  the  body  of  the  sun  as  a  whole.  The  apparent^ 
flat  surface  presented  by  a  view  of  the  photosphere  is  caUed 

the  sun's  dUk.  ,     ,    ,.      .  , 

Bpoto.— When  the  photosphere  is  exwmnedwith  a  tele- 
nope  small  dark  patches  of  varied  and  irregular  outlme 
I^^iJ^ilyfouiduponit.    These  a^caUed  the  «*«. 

'bIiMIoii.— When  the  spots  are  observed  from  day  to 
day,  they  are  found  to  move  over  thesun's  disk  in  sudi  a 
w/y  M  to  show  that  the  sun  rotates  OB^t.  aas  in  a  period 

ofWoraedays.  The  sun,  therefore,  hsa  «*»,  iw<^,  «« 
^„«ter,  Uke  Ae  earth,  the  axis  being.the  line  around 

which  it  rotates.  uj  j.4«  a-,  a* 

f^MWl».-Groupe  of  minute  speeks  bri|0itor  than  tte 

tood  of  ipotoOT  elsewhere.    They  aw  oilled/«»«lA 


FSATURMB  OF  ThJ  BUN. 


279 


hXT. 

armed  with  the 
modern  science, 
iraried  and  complex 
le  phenomena  to  be 
ount  of  the  physical 
nmary  of  tlie  main 
>ody. 

n  the  mm  presents 
visible  shining  mr- 
|;A«r0,todistingaish 
e.  The  apparently 
photosphere  is  called 

xamined  with  a  tele- 
ad  irregular  outline 
are  called  thoMZor 

served  from  day  to 
sun's  disk  in  such  a 
nits  axis  in  a  period 
,has«Bi«,iw2Wf  and 
iug  the  line  around 

a  brin^i^nr  Uian  the 
leen  in  the  neif^bor- 
re  aOkd/dMilai. 


CHuromoaphMre,  or  Uamu — The  soUr  photosphere  is 
covered  by  a  Uyer  of  glowing  vapors  and  gases  of  very  ir- 
regnhur  depth.  At  the  bottom  lie  the  vapon  of  many 
metals,  iron,  etc.,  volatilized  by  the  fervent  heat  which 
reigns  there,  while  the  upper  portions  are  composed  prin- 
cipally of  hydrogen  gas.  This  vaporous  atmosphere  is 
conmionly  called  the  ohromoapheref  sometimes  the  tierra. 
It  is  entirely  invisible  to  direct  vision,  whether  with  the 
telescope  or  naked  eye,  except  for  a  few  seconds  about 
the  beginning  or  end  of  a  total  eclipse,  but  it  may  be  seen 
on  any  clear  day  through  the  spectroscope. 

Fromlnenoss,  Protuberano— ,  or  Bed  Tiaacaam. — ^The 
gases  of  the  chromosphere  are  freffuently  thrown  up  in 
irregular  masses  to  vast  heights  above  the  photosphere,  it 
may  be  500,000,  100,000,  or  even  900,000  kilometres, 
like  the  chromosphere,  these  masses  have  to  be  studied 
with  the  spectroscope,  and  can  never  be  directly  seen  ex- 
cept when  Uie  sunlight  is  cut  off  by  the  intervention  of  the 
moon  during  a  total  eclipse.  They  are  then  seen  as  rose- 
colored  flames,  or  pUes  of  bright  red  clouds  of  irregular 
and  fantastic  i^pes.  They  are  now  usually  oalied  "  prom- 
inences" by  W^  English,  and  "protuberances"  by 
French  writers. 

Cknmia. — ^During  total  eclipses  the  sun  is  seen  to  be  en- 
veloped by  a  mass  of  soft  wldte  light,  much  fainter  than 
the  diromosphere,  and  extencting  out  on  all  sides  far  be- 
yond the  hi^est  pfrominences.  It  is  IwighteilliRNind  the 
edge  of  the  son,  kdA  UdMoft  toward  its  outer  hoondaiy, 
by  iuensiblegradatleiis.  This  halo  of  lig^t  is  ealled  the 
wrmO)  and  is  a  v«7  sfarikiBg  object  dnringatotal  eeUpee. 


MpeekaadStraotwMoftlMllMtoqplMr*^— The  disk 
of  the  son  id  einnlar  in  shape,  no  matter  ytfoA  aide  of  tiie 
sub's  §^obe  is  turned  toward  us,  whence  it  follows  duijt^ 
SUB  itself  is  a  sphere.    The  aspect  of  the  disk,  when 


380 


ABTBONOMr. 


viewed  with  the  naked  eye,  or  with  a  toletoope  of 
low  power,  is  that  of  a  uniform  bright.,  shining  Hurfaoe, 
hence  called  the  photoaphere.  With  a  telescope  of 
higlior  power  the  photospliere  is  seen  to  be  diveraified 
witli  groups  of  spots,  and  under  good  conditions  the 
whole  mass  has  a  mottled  or  curdled  apiwaranoe.  This 
mottling  is  caused  by  the  presence  of  cloud-like  forms, 
whose  outlines  though  fidnt  are  yet  distinguishable. 
The  background  is  dso  covered  with  small  white  dots 
or  forms  still  snudler  than  tlie  clouds.  These  are  the 
"  rice-grains,"  so  called.  The  clouds  themselves  are 
composed  of  small,  intensely  bright  bodies,  irrq^larly 
distributed,  of  tolerably  definite  shapes,  which  seem  to  be 
suspended  in  or  superposed  on  a  darker  medium  or  back- 
ground. The  spaces  between  the  bright  dots  vary  in 
diameter  from  2'  to  V  (about  1400  to  9800  kilome- 
tres). The  rice-grains  themselves  have  been  seen  to 
be  composed  of  smaller  granules,  sometimes  not  more 
than  0''8  (186  miles)  in  diameter,  clustered  together. 
Thus  there  have  been  seen  at  least  three  orders  of 
aggregation  in  the  brighter  parts  of  the  photosphere : 
the  laiger  cloud-like  forms ;  tiie  rice  grains ;  and,  soDoall- 
est  of  aJI,  the  granules.  These  forms  have  been  studied 
with  the  telflsoope  by  Sboohi,  Hvoons,  and  Lakolit, 
and  their  relations  tolerably  well  made  out. 

In  ths  Amuuin  of  ths  Bureau  of  LoMtitiidss  lor  187B  fo.  089). 
M.  J  AMiSBH  givM  an  soMunt  of  hk  rsosaft  OMKivsiy  of  the  NttBttlatod 
amngoMBt  of  tlM  solar  photospbcN.  Ths  pi^sr  is  aosotipMMsd 
by  a  jdwtograph  of  ths  appeanasas  dcserlM,  wUoli  Is  «ilaif«d 
thraefold.  Pnotogn^th*  uas  than  four  IboImS  la  msiMfcif  cannot 
ntkfaotorily  show  meh  tfslafle.  As  the  mwAitlsBsef  >  the  sOhr 
Mirfaoe  an,  in  goMral,  not  graatiy  Isrger  thaa  1"  or  W,  th*  photo- 
graphic imdisSon,  which  is  soowtiBBCs  M"  o#  mtan,  im^  caBsphtety 
obwuM  their  eharsetcriatf ei.  This  dtflooHv  M.  Jamshw  has  over- 
oome  bj  enlarging  the  image  and  shortaanig  ihe  thae  of  czpos- 
ure.  In  this  way  the  irmfflstion  is  dfariMMted,  beeaan  m  tls  dt- 
ametcis  increase,  the  linear  dimensions  of  the  details  ars  towaassd, 
and  "  the  imperfections  of  the  sensitive  plats  havs  iM  nlative  iss- 


h  a  toleioope  of 
k,  shining  Burf»ce, 
[   a   telescope    of 

to  be  diversifled 
)d  conditions  the 
piMjaranoe.      This 

cloud-like  forms, 
it   distinguishable. 

small  white  dots 
i.  These  are  the 
ds  themselves  are 
hodies,  irregularly 
,  which  seem  to  be 

medium  or  back- 
right  dots  vary  in 
)  to  2800  kilome- 
kave  been  seen  to 
metimes  not  more 
clustered  together. 
St  three  orders  of 

the  photoaphere : 
gruns ;  and,  amall- 
s  have  been  studied 
»»8,  and  Lamolbt, 
tout. 

Idas  lor  1898  ^  ««»)• 

IMS  la  tfasuliit  cauiot 
HHMlatisMQftbs  solMr 
ta»il"ofr,tl»l*o4o. 
oi  awa,  SMJ  oompleUjly 

fiwihstime  of  npof 
h&beea«aastl!a«- 
liadstaUssiahiewsssJ. 
Its  bava  Ms  rdattva  Un- 


Htrif'a 


Affain,  M.  jAWSsaif  has  noted  tlwt  in  short  expomira  the  photo* 
gnpnic  •pectnim  it  slmoat  monochiomatio. 

In  this  wsy  it  differs  greatly  from  the  visible  spectrum,  und  to 
the  advantage  of  the  former  for  this  special  purpose.  The  diameter 
of  the  solar  photograms  have  since  1874  been  successively  increased 
to  12,  IS,  90.  and  80  centimetres.  The  exposure  is  made  equal  all 
over  the  surface.    In  summer  this  exposure  for  the  largest  photo- 


282 


ABTRONOMT. 


urt'  genenlly  circles  or  ellipiea,  but  these  curres  «re  sometimes 
gresUv  altered.  This  ^nuialstion  is  ftpparently  spread  equally  all 
o^er  the  disk.  The  brilliancy  of  the  points  is  very  variable,  and 
they  appear  to  be  rituated  at  different  depths  below  the  photo> 
sphere  :  the  most  luminous  particles,  those  to  which  the  solar  light 
is  chiefly  due,  occupy  only  a  small  fraction  of  the  solar  surface. 

He  most  remarkable  feature,  however,  is  "  the  reticulated  ar- 
rangement of  the  parts  of  the  photosphere."  "  The  photo^rams 
show  that  the  constitution  of  the  photosphere  is  not  uniform 
throughout,  but  that  it  is  divided  in  a  series  of  regions  more  or 
less  distant  from  each  other,  and  having  each  a  special  constitution. 
Thew  regtoDB  have,  in  general,  rounded  contours,  but  these  are 
often  slflMMit  rectilinear,  thus  forming  polygons.  The  dimensions 
of  these  flgnres  are  veiy  variable ;  soma  an  even  1'  in  diameter 
(over  MLMO  miles).'*  "Between  thew  flgorea  tiia  grains  are 
sharply  defined,  but  in  their  interior  tliqr  b«  almost  eAiced  and 
run  tof^rther  as  if  by  some  force."  These  phenonMna  can  be  best 
underrtood  by  a  reference  to  tiM  figure  of  1l  jAnsanf  (p.  Ml). 

Light  ■Dd  HMife  ftom  tbm  VliotoiplMra. — ^The  fholo- 
sphere  is  not  equally  bright  all  over  the  apparent  disk. 
This  is  at  onoe  evident  to  tite  eye  in  observing  the  snn  with 
a  telescope.  The  centre  of  the  disk  is  most  brilliant,  and 
the  edges  or  limht  are  shaded  off  so  as  to  f (Mreibly  suggest 
the  ids*  of  m  absorptive  atmosphere,  which,  in  £iot,  is  the 
canse  of  this  appearaaoe. 

Bncb  absorption  ooonn  not  tmly  for  die  rays  by  which 
we  seethe  son,  the  so-called  wmmA  ra^f  bat  tor  those 
which  have  the  most  powerfnl  effect  in  deoomporing  the 
salts  of  silver,  the  so-MUed  i^emioal  royt,  by  whidi  the 
ordinary  j^K^ograph  is  taken.    • 

The  amonnt  of  heat  reoeived  imm  WbawA  portions  of 
the  son's  disk  is  also  variaUe,  Mowding  to  tita  part  of 
the  a^Nurent  disk  examined.  This  ia  what ««  shoiikl  ex- 
pect. Thatis,!ftheiiiteo[^ofiaiy4»eof  tlMsendi«ttons 
(as  felt  at  the  eartili)  varies  from  centre  to  oironmferunoej 
that  of  every  other  shonld  also  vary,  since  they  an  all 
modifications  of  the  same  primitive  moti<m  of  the  son's 
constitnent  particles.  Bot  the  cottstitation  of  tiie  son's 
atmosphere  is  soch  that  the  law  of  variation  fw  the  lluree 
dassea  Js  different.  The  intensi^  of  the  radiation  in  the 
son  itself  and.  inside  ai  the  absolve  atmosphaiie  is  i»<qb» 


..:m^^. ...>...■.-.    -.^^-    ,.     ............. -^.^.^v,^   «.^.^.    ..■„...-.,■■■.   --.,...,^«.,-  ........   ^^....^^^1^ 


unres  are  ■ometimes 
tlj  spread  equally  all 
ii  very  Tariable,  and 
M  below  the   photo- 
whicb  the  solar  light 
the  Bolar  surface, 
"the  reticulated  ar- 
"The  photograms 
here  is  not  uniform 
s  of  reigns  more  or 
a  special  oonstftuiion. 
intoarajbut  these  are 
MM.    The  dimensions 
I  erea  1'  in  diameter 
gnns  the  pains  are 
rs  almost  dnced  and 
kenomflna  can  be  beat 

jAMtBN  (p.  Wl)> 


BOLAR  BADIATIOir. 


283 


iMr*.— The  . 
the  apparent  disk, 
lerving  the  snn  with 
most  brilliMit,  and 
to  f  <Hrcibly  raggest 
rhioh,  in  &ot,  is  lihe 

r  the  fmjB  by  which 
ray«,  bat  fur  those 
in  decomposing  the 
roftf  by  which  the 

difiereufc  portions  of 
^ding  to  tile  part  of 
what  we  ilioald  ex- 
M  of  ^flseaiiitioDB 
re  to  circnmferuneei 
r,  since  they  an  all 
mo^oa  of  tiie  sun's 
titationof  the  Kin's 
nation  for  tiie  tfoee 
the  radiation  ill  tlie 
«  atmos||^h«Ri  ii  1^^ 


ably  nearly  constant.  The  ray  which  leaves  the  centre  of 
the  sun's  disk  in  passing  t-o  the  earth,  passes  through  the 
smallest  possible  thickness  of  the  solar  atmosphere,  while 
the  rays  from  points  of  the  sun's  body  whidi  appear  to 
us  near  the  limbs  pass,  on  the  contrary,  through  the  maxi- 
mum thickness  of  atmosphere,  and  are  thus  longest  sub- 
jected to  its  absorptive  action. 

This  is  plainly  a  rational  explanation,  since  the  part  of 
the  sun  which  is  seen  by  ns  as  the  limb  varies  with  the 
position  of  the  earth  in  its  orbit  and  with  the  position  of 
the  sun's  surface  in  its  rotation,  and  has  itself  no  physical 
peculiarity.  The  various  absorptions  of  different  classes 
of  rays  correspond  to  this  supposition,  the  more  refrangi- 
ble rays  suffering  most  absorption,  as  they  must  do,  being 
composed  of  waves  of  shorter  wave  lengtii. 

The  following  table  gives  the  observed  ratios  of  the  amount  of 
heat,  light,  and  cheidcal  action  at  the  centre  of  the  sua  and  at 
raiioas  diataaoea  from  the  centre  toward  the  Umb.  The  flrst 
column  of  the  table  ^ves  .the  a^iarent  distaneea  from  the  centre 
of  the  disk,  the  san*s  radios  being  1*00.  The  second  oohum  gives 
the  peroentage  of  heat-raya  recced  by  an  obsiTrer  on  the  earth 
from  pdnts  at  these  various  diatances.  That  ia,  for  every  100  heat- 
raya  reaching  the  earth  from  the  san*a  owtro,  M  teach  ua  from  a 
point  lialf  way  from  the  centra  to  the  limb,  and  so  on. 

AttSlMous  data  an  given  for  the  IMit-nqrs  and  the  ehamical 
raya.  Ae  data  in  regud  to  heat  are  mw  to  Prof enor  LMMatMi : 
those  in  regard  to  li|^t  and  chemical  action  to  Prof  essor  Pzoxaawo 
and  Dr.  Voobl  tmpeMnlj, 


PwfAWCT  mem 

Cmw* 

EastSsgra. 

ligktB^ri. 

OhnUcatB^Mw 

e-eo 

100 

m 

OS 

80 

•  •  *  • 

•  •  •  ' 

OS 
80 

•  •  •  • 

100 
Wt 

m 

55 

•  «  •  • 

•  ■  •  • 

87- 

100 
88 
80 
86 
46 
95 
» 
18 
18 

9.aB 

9.n... 

0>t6 

0.tB 

0.M 

0.tt. 

1-00 

•   iKir  tmo  equal  a^arant  sorfaeea,  A  aear  the  saa's  osatra  sad  B 
mm  Hm  UndH  w*  Mqr  mf  tkat  the  nt*  <>«»  tiio  tiwaoiiaaas  wtai 


ASTRONOMY. 


j 


I- 


raoeired  at  the  earth  hare  approximately  the  following  relatire 
effects: 

A  has  twice  as  much  effect  on  a  thermometer  as  B  (heat); 

A  has  three  times  as  much  illuminating  effect  as  B  (light); 

A  has  seven  times  as  much  effect  in  decomposing  the  photo- 
gratriiic  salts  of  silver  as  B  (actinic  effect). 

It  is  to  be  carefully  borne  in  mind  that  the  above  numbers  refer 
to  vwdations  of  the  sun's  rays  received  fma  different  equal  surfaces 
A  and  B,  in  their  ^*et  vpon  etrtam  atiUrary  Uri'MtritU  tUmdarda  qf 
mmuurt.  If,  for  example,  the  decompoduon  of  other  salts  jthan 
those  employed  for  ordinaiy  jphotogrannic  worlc  be  taken  as  stand- 
ards, then  the  numbers  will  be  alteraa,  and  so  on.  We  am  simply 
measuring  the  power  of  solar  rays  selected  from  different  parts  of 
the  sun's  apparent  disk,  and  hence  exposed  to  different  condiitions 
of  absorption  in  his  atmosphere,  to  do  work  of  a  certain  selected 
kind,  as  to  raise  the  temperature  of  a  thermometer,  to  affect  the 
human  retina,  or  to  deconipose  certain  salts  of  silv«r. 

In  this  the  absorption  of  the  earth's  atnioephere  is  rendered  con- 
atut  for  each  kind  of  experiment  This  ataiosphere  has,  however, 
a  vary  strong  abswptive  effect  We  know  that  we  can  look  at  the 
aettiag  or  rising  sun,  which  sends  its  lij^t  rays  through  grmt 
deplka  of  the  ewth'a  atOMMqpliere,  but  not  upon  the  sun  at  noon* 
day.  Tke  temperature  is  lower  at  sunrise  or  at  sunset  than  at  noon, 
and  tlM  absorption  of  chemical  rwsis  so  marked  that  a  ^lotograph ' 
of  the  solar  spectrum  which  can  be  taken  in  tiiree  seconds  at  noon 
requires  six  hundred  seconds  about  ■unset— that  is,  two  hundred 
tinea  as  long  (Dbafbb). 

Amoimt  of  Haat  amitfead  bf  the  Bun.— Owing  to  the 
absorption  of  the  aohur  atmoqilierB,  it  followa  that  we  re- 
eeive  only  *  portion— peihapa  «  yeiy  small  pwtion  —  of 
the  rays  emitted  by  the  snn's  |iiotoq>here. 
^  If  the  snn  had  no  absorptiTe  atahosphen,  it  would  seem 
to  IIS  hotter,  brighter,  and  more  bine  in  color. 

Exact  notions  as  to  hoir  grtit  ibis  absorption  is  are  hard 
to  gain,  but  it  may  be  said  fm0y  thai  the  beat  authori- 
ties tgree  that  althoni^  it  irffillii  possible  that  the  son's 
«t«Mv)kere  abaoibs  hatf  tt*4iPed  nj^ 
not  absorb  four  fifths  of  tbMil. 

It  k  a  cnrions,  and  as  yet  if«i  bdiave  vnaxiMiMd  lMt» 
tiiat  the  absorption  td  iSb»  silfiM^iitmosphairedoes  nut  iplofc 
the  daritness  of  the  FnMnhelaar  fines,  ^nicy  seam  «0B^ 
UmsIe  at  the  eentie  and  e%B  ef  the  san.*    fkmi 


Prol.  TovMihaa 


ofa 


I. 


nut  rlHi»lniiiffiilfilHhlllliiwMft| 


HEAT  OF  THB  SUIT. 


m 


le  following  relatire 

vtt»B  (heat); 
ct  18  A  (light); 
omposing  the  photo- 
above  numben  refer 
iflerent  equal  mrf aoea 
tw  iiMff fcrf  itandanU  ^ 
■  of  other  aalta  jkhaa 
ark  be  taken  a*  ttand- 
10  on.  We  are  simply 
rom  different  parts  of 
o  different  oondiitiona 
c  of  a  certidn  aelected 
IOmeter,  to  affect  the 
f  diver. 

ibere  is  rendered  con- 
oaphere  haa,  however^ 
lat  we  can  look  at  the 
it  rays  throngh  great 
p<m  the  sun  at  noon' 
tt  sunset  than  at  noon, 
ked  that  a  photograph 
three  seconds  at  noon 
4hat  is,  two  hundrad 


im.-— Owing  to  the 
foUowi  that  we  ra- 
anaU  portion — of 
lera. 

)here,  it  wonld  seem 
in  color. 

ibsorption  is  are  hard 
lat  the  best  aothori- 
Mible  that  the  son's 
^  it  probably  does 

m  nnexplabMd  lMt» 

pbeife  does  nut  i^set 

They  seem  efpl^ 


of  this  absorption  is  a  practical  question  to  ns  on  the  earth. 
So  long  88  the  central  body  of  the  snn  continnes  to  emit 
the  same  quantity  of  rays,  it  is  plain  that  the  thickness  of 
the  solar  atmosphere  determines  the  number  of  such  rays 
reaching  the  euth.  If  in  former  times  this  atmosphere 
was  much  thicker,  then  less  heat  would  have  reached  the 
earth.  Professor  Lanolkt  suggests  that  the  glacial  epoch 
may  be  explained  in  this  way.  If  the  central  body  of  the 
sun  has  likewise  had  different  emissive  powers  at  different 
times,  this  again  would  produce  a  variation  in  the  tempera- 
ture of  the  earth. 

Anmmt  of  Heat  Badiated.— There  is  at  present  no  way 
of  determining  accurately  either  the  absolute  amount  of 
heat  emitted  ^m  the  central  body  or  the  amount  of  this 
heat  stop]>ed  by  the  solar  atmosphere  itself.  All  that  can 
be  done  is  to  measure  (and  that  only  roughly)  the  amount 
of  heat  really  received  by  the  earth,  without  attempting  to 
define  aecvrately  the  drcnmstiaoes  which  this  radiation 
has  undergone  before  reaching  the  earth. 

The  difficulties  in  the  way  of  determining  how  ni  iioh 
heat  readies  the  earth  in  an|  definite  time,  as  a  year,  are 
twofold.  Hist,  wemnsl  J»ilAe  to  distinguish  betwew 
the  heat  as  received  by  •  tiiermometrio  apparatos  from 
the  smi  itself  and  that  from  external  objeete,  as  onr  own 
atmosphere,  adjaoent  bnUdings,  ete.;  and,  second,  we 
must  be  sible  to  aDow  fw  the  absorption  of  the  eardi's 

Fotnujff  has  Mperimenled  spoa  this  qaestisiiviwiWng 
i^owaaee  for  the  tfane  that  tiie  nm  is  below  (Imi  Iioriaoo 
of  wbf  ^ha$,  and lor  tluf  taet  tkstt  the  solar  my»4»  Mfr^ia 
geiMil  ttiiieB  pmfml&eii3mAj  b«ft  obUqvely  i^  any 
gifW ipai!t of  dearth's  sailMe.  His^oomflnsloni  msgr 
IM  alM  as  laBows :  if  our  0(1^  atmiMfiiere  were  re- 
laolMdi  liM  BOkf  figrt  wwdd  hvn  emigy  enongfa.  to  nielt 
m  igfir  of  lee  9  eenlimotfai  thidc  over  j^  whole  eaitii 
ill^^«li^«rotali0itt:«»iin»^ti^^  '  : 

atittleltl  anooBl  oTImI  radiate*  %  the  aim,  flao 


3M 


■^•T' AJ^"     !-'      ■       '■''' 


^iimmitfitmitt^iatmm 


m 


ASTBONOMT. 


earth  receivea  but  an  inBignificant  share.  The  son  is 
capable  of  heating  the  entire  Bnrface  of  a  aphere  whose  ra- 
dins  ia  the  earth's  mean  distance  to  the  same  degree  that 
the  earth  is  now  heated.  The  surface  of  such  a  sphere  is 
»,170,000,000  times  greater  than  the  angular  dimensions 
of  the  earth  as  seen  from  the  sun,  and  hence  the  ewih  ref 
ceiyee  less  than  one  two  billionth  part  of  the  solar,  radia- 
tion. The  rest  of  the  solar  rays  are,  to  far  as  we  know, 
lost  in  space. 

It  is  found,  from  direct  neMiires,  that  a  ■on-qwt  riTM  1«P  ^«^ 
MM  for  area;  tiMUl  the  unepotted  photoaphere,  and  »*  *■  "jnj^^- 
h^mJomYum  much  thTeUmAe  of  tlie  earth  can  be  affected  by 

ProfeeMV  Laxolbt,  of  Htteburgh,  hM  made  meuuieinento  of  the 
dlwcteihet  of  eon-epote  on  tcrreetrW  temperature.  'n»-<**^_^ 
SonTcoadeted  to  mSJurtogtherelyflTeywrnteofumbra^ya^ 
h^udnhotaaDherieradiatkm.  TherelaliTeumbnd,  penmdmL 
IS  phSJSSTSL  were  deduced  from  the  g«w  obeemgoue  of 
!Se  r  «31*om  a  conrideratlon  of  thcMi  data,  and  ccaftoiBg  0» 
SSSkm^to^to  changwof  temetrial  temperature  doe  to  this 
SSTSbSjSiSjSr  dSuce.  the  .«ult  that  "  ««»-«P«*- J«  «- 
MMM aSroct  effect  on  terreetrW  temperatare  by decrcMiM  the 
^teSieMeof  the  earth  at  their  marimum."  l^toS-K 
SrSSSSTW^-wU,  aa  "  it  U  repieiented  by  a  change  to  tEe 

thadilt.  on  the  whole,  oootar  to  narinnm  ■••■^.  y*^"?*. 
Sy?i2rJ^M»«MMMjroea  it  tends  to  mafce  the  wrth  ^^^ 
SS^ASteauouBt     What  other  cau«s.«»y  co«riit  with  the 


IHfiy,  VampaMfeoM.— -Froo  the  amoiint  of  heat  iotaa]^ 
ndJKtedby  tiM  a^  altetopta  haw  be«iimideted«ton«to» 
tbi  Mtaal  teupeMtare  of  tiie  K^lar  ratftee.  Tlie  Mil- 
uMlMMMlifldbyTariuu  anUioritiei  dilleriride|y, « tkft 
Imn  «Ueh  gomn  tlw  abaoviit&ea  iwiOiiii  Oit  *Mbr  m- 
Tiiop*  an  aknart  unknown.  Soma  mmIi  hmM  ablM^ 
m^hm  to  beampoaed  in  any  mill  imrmtiffUmttaA^ 
MtfaMtea  htm  muni  iHNMy  MooMttiig  to  «iM  li^ftea 
Imp. 


iimmitk 


8P0T8  ON  THE  aUJT. 


S87 


share.  The  son  is 
of  a  sphere  whose  ra- 
the same  degree  that 
se  of  such  a  sphere  is 
e  angular  dimemdons 
id  hence  the  earth  re? 
irt  of  the  solar,  n^a- 
I,  CO  far  as  we  Itnow, 


a  nin-apot  giru  l«p  |ieat, 
here,  and  it  is  an  ioterett- 
e  esrth  can  be  affected  by 

nade  meamiementa  of  the 
mperatore.  The  obeervv 
■KHUits  of  umbral,  pemmi- 
latire  umbral,  peBmabral, 
m  the  Kew  obMrratloiM  of 
data,  aad  oonflniBg  the 
tempentofe  doe  to  this 
..  tiiat  "  soB-Rpots  do  ex- 
entare  by  decreadiw  the 
Mzimitm."  Tliia  cbaiiae 
leuted  byaehaiHp  in  Um 
en  yean  not  gmOtr  than 
I  not  intended  to  show  that 
dmrnn  MUMpot  y«M,  iMt 
»  make  the  f«rtb  eooler  br 
MS  nay  oo^eiist  wMi  the 


amount  of  heat  «otiN^7 
been  made  todfOtemfo* 
\u  nabm.  The  mH- 
MaUleriride^,MtlM 
1  iwithto  tlit*Mlar  <■»• 

Bofe«bN|«i»  tiwiii^ilta 
»«i«bo«t^lOO»OOOP  0. 


philosophy,  tLe  temperature  must  far  exceed  any  ter- 
restrial temperatnre.  There  can  be  no  donbt  that  if  the 
temperature  of  the  earth's  surface  were  suddenly  raised  to 
that  of  the  sun,  no  single  chemical  element  would  remiun 
in  its  present  condition.  The  most  refractory  materids 
would  be  at  once  volatilized. 

We  may  concentrate  the  heat  received  upon  several  sousre  feet 
(the  snrnce  of  ahiue  Iraming-Iens  or  mirror,  for  instance), 
ezsaine  its  effects  at  me  focus,  and,  makinip  allowance  for  the  con- 
densation by  the  lens,  see  what  is  the  minimum  possible  tempera- 
ture of  the  son.  The  temperature  at  the  focus  of  the  lens  cannot 
be  hiriier  than  that  of  <:lie  source  of  heat  in  the  sun  ;  we  can  only 
concentMie  the  heat  neeived  «■  the  snCMe  of  4m  Imb  to  one 
point  and  examine  iU  effects.  If  a  leas  three  feet  In  dlMMter  be 
hsed.  the  most  refractory  materials,  as  flf»«lay,  jdatimnb  the  dia- 
mond, aia  at  once  melted  or  valatiUasd.  The  effect  <tf  Hw  lens  is 
phdnlythei  "  "         '"  * 

the  ra " 
the 


mond,  aia  at  once  melted  or  valatiUasd.  The  effect  <tf  Hw  lens  is 
phdnly  the  same  as  if  the  earth  wan  brai^t  doesr  to  tta  sun,  fai 
the  ratio  of  the  diameter  of  thafoDatimage  to  that  of  the  tins.  In 
the  case  «t  tho  lens  of  thres  Isat,  aflowiiw  for  the  absorjpMM,  etc., 
this  dManeeis  yet MMler than  fhatot  tha  moon  tnmltte  east, 


so  that  tt  appean 
sun,  if  eamposedof 
beTUflriaed. 
If  wa  oaleolate  at  what  rate  the 


MWMt  ar  plaaat  so  dose  as  ttli  to  the 
'   "     to  tlioee  kk  the  eim,  must 


lofthesoaiioaldbe 


lowered  Annually  by  the  radlatkm  fraas  itaattftM^  we  M  And  it 
to  be  U*  Centigiade  yearly  If  itt  sMdle  teat  la  imM 
ud  be^mn  fuA  «•  peraaan  tf%WM^  •^  *"  ^  ' 


water, 

tiiat^liMTariaiisooiis&tiie^  ItiSdtheie- 

fore  oool  down  la  a  few  thoasaad  yean  by  an  appasdaMa  MBOOiit. 


i  8. 

A  very  cnnory  ex«mina:don  of  the  ran's  disk  with  a 
Bindl  IdflMepe  witt  gMMidly  show  one  or  mora  da^  i|Mii 
uMm  tltepliOtMiilien.  Then  are  of  vMiMMirini»  fran 
ntante  m^  dote  1'  or  9*  in  diameter  (IMO  Irilomelm 
otf  iM^  40  llilie  ipoli  wveral  mimitM  of  ara  ki  eiMa*, 

Selftr  apoli  fBiiewBy  luwe  a  dM*  eenteJ  iimfliiir  »r 
umkm^  Mrroqadedby  a  border  or  pmmim  ol  ffi^ 
thU,  tetemedtrte  fai  dMde  tetween  tifo  iiM  lilMtoMi 
and^die  lN%fitl  phoioiplMvo.  ^  ii 
H>e  UliiBMp*,  ^  ilMii  ■-  mm  ♦»»  <>»:#»^ 


MiiH*MiitilH«MiMd«lri^^ 


I8S 


ABTRONOMT. 


and  is  BometimeB  crossed  by  bridges  or  ligaments  of  sliining 
matter.  The  penumbra  is  composed  of  filaments  of 
brighter  and  darker  light,  which  are  arranged  in  striae. 
The  appearances  of  the  separate  filaments  are  as  if  they 
were  directed  downward  toward  the  interior  of  the  spot 
in  an  oblique  direction.  The  general  aspect  of  a  spot  un- 
der considerable  magnifying  power  is  shown  in  Fig.  78. 

The  first  printed  account  of  solar  spots  was  given  by 
FABBrmrs  in  1611,  and  Oauleo  in  the  same  year  (May, 
1611)  also  described  th«n.     They  were  also  attentively 


fro.  W.-'xmwmk.  tarn  rxmaamk  m  mm-wrvi. 


rtncUied  by  Hm  Jesnit  SoaimBB,  wli»  Ji^^fQMd  tbem  to  b< 
■auOI  pli^  projected  agiiiHt  tibe  tOaf^SO^  Thb  u 
WM  diiprofved  by  GAUtun,  whoM  oiwlyittofti  dMfW 
tfaann  to  belong  to  tiie  ann  itself,  ^tad  lo  imif^  iiiiipi«4) 
MRNitlieMlardiakfromewfctoimt.  A  tpo||«t  iHrifel« 
it1lM»«Hit  faib  of  the  mm  on  iittyifM.4l^]teKtm 
MKOH  Hie  (fide  lor  IS  or  1^  diqri^Aa"iliiilditJ:tili>liii 

jp«riod»  itiMfiptesd  aft^^^lhb  «Mtai»la^ 
lid  aiior  it  Iwd  iii  lite  vmm^mniMmA. 


.ii^ 


■•■'■  "-"'li'  1 1  'ih  -■•■'*  ■'■'i-rT-irfi'fi"  ■'iu'a 


rr. 

68  or  ligaments  of  sluning 
mpoBod  of  filaments  uf 

are  arranged  in  striee. 
)  filaments  are  as  if  they 

the  interior  of  the  spot 
neral  aspect  of  a  spot  nn- 
er  is  shown  in  Fig.  78. 
Bolar  spots  was  given  by 
in  the  same  year  (M4y, 
ley  were  also  attentively 


8UjrB  SPOTS  AND  ROTATION. 


289 


,  whoittpfQMd^hemtQlM 
«he  sobi'diik..  TiBkMm 

f ,  jAiid  lo  wem^  larffcrtnljr 
vim.   AllSridKM^^MiMM 


The  spots  are  not  permanent  in  their  nature,  but  are 
formed  somewhere  on  the  snn,  and  disappear  after  lasting 
a  few  days,  weeks,  or  months.  But  so  long  as  they  last 
they  move  regularly  from  east  to  west  on  the  sun's  appar- 
ent disk,  making  one  complete  rotation  in  about  25  days. 
This  period  of  25  days  is  therefore  approximately  the  rota- 
tion  period  of  the  sun  itself. 

Spotted  Bagion.— It  is  fonod  tbat  the  qwts  are  ohiafly  eoa- 
flned  to  two  soBct,  one  in  each  hemliphere,  •ztending  from  about 
10°  to  8S*  or  40*  of  helfogia]^  latitoclfl.  In  the  iMlar  regions, 
Bpotsansearoelj  ever  wen,  and  on  the  sobr  equator  tliey  are  much 


fW.  Tl>.^ 


i>tth 


of  tke 


lyffca.-ipr- 


ntoathaii  iv^'la^Mtai  iy  a(in#  iht-i 
pMi.  hot  Mm  0*  or  'rtiiWillii.  #ilar  i 

•  tte  pfltH  wteo  t\e  sii^  It  i 

b  dM^  iha  aaasC  fari«def  IMidafiyfiii 

,  -u  .>..  'tail  MaiaeACMtft'ilkHMiaiaMi'i 


iaiiMiinifiiiiinmr 


i   ■■  iiiilAiiitittailSiiiili 


too 


ASTROirOMJ. 


■olar  equator.  A  BeriiM  of  obMiratiom  made  by  Mr.  Cabbihotoii 
of  SnglKDd  (by  the  eye)  give  the  following  values  of  the  rotation 
tlnyM  T,  tot  spots  in  different  heliographic  latitudes  L  : 


r<=MOM  M-89e 

Tab  period  of  rotation 


10* 


15° 
S5-800 

97MS 


45* 


alio  to  Tary  ionewhat  in  <Uflertat 


TAB  period  of  rotation  Mema  aiao  lo  vary  sonewnac  m  iguinnini. 

Sh  eaMwt  JSn  any  OM  dalaitoMtatkM  ti»*  to  the  an,  la 
^mMM  to  Mm  MOth  or  tha  aMOo. 

""IbovralMbiUtyiathattheMU^  iiotMM«oUd,l"Mi^VMefM 
period  of  roUtion,  but  dtflBfOit  portioiia  of lu  surface  and  of  ita  in- 


a'atain  of  th*  Spoil.— Hie  mm-qxits  are  redly  depNi- 
lieitaW&epliotMpliflW,  ww*»  int  fdfaiAMl  <M  ligr  iof- 

elUptioit  &  ahype.  Am  the  rotatton  «iHnp|iH  H  fidlilMr  i^ 
fBvdMv  mk  i»  th*  diiky  it  beoomM  moi»  aad  mote  neulj 
dfwa«r  te  (*ife, -ii  .Iter  fertsr%«ili»  el  11-^^ 
Am  •ppaMEMMs  take  pteoe  in  revwie  oMv. 


teHdr  dirtt  ooor  mm,  wnouiiaWl  W 


ss 


ude  by  Mr.  OARBiifOTON 
IS  valuca  of  the  rotation 
B  Iktitudes  L : 

IB" 
2n-500 

W 

97WS 

awMiiewlwt  in  <UflartBt 
itioa  tbM  to  tlM  «n,lt 

KaoUd,  hMNtUf  M  *m 
U  lurface  «id  of  MU  m- 
>  titont  1»<i»MiMlwi t- 


ipote  are  redly  Hiaftm- 

R  isitff tw  it  fnnMr  Ji|M 

int  oioir. 

rwo  b^inni  of  elN 


■Mviiitii 


HM  ASTROKOMT. 

tnl  Md  MUd  nucleu.to  the  J""  ». "°J^  J°°J",^tlY  by  ^rwt. 
The  .pp«ently  bl«k  centre^  <*eBgjta»w^«^^^ 

ftitpMr  Tery  bright,  h  >»•  ^'^  P!^T~  ii&  nucW  beneath  «ich  an 
or'Kofe-or  ^^^"'"'■^^J^  iJSld  won  become  gM«>«»J»y 

ninplT  of  «>»«>' »»?*'^*?f*',J^  STM^iiStuted  haw  •endbly 
the'Brtorto  period,  wouM  to  a  «,  ^^J^J'SS  other  !«•«>«. 
aiHrfaUbed  to  a  few  hundred  7*^.*^^JS^  Mve  at  to  the  fMt 
4j!ri»»n*iMda  of  HBiaoHBL  most  be  modmea,  »▼«  ■■  w  •m- 
{S»  gS^^  SSySSttoi  to  the  photoephere. 


mice  of  cloudy  and  clew  ye-r.  on  tte  ^h.  :^^^^ 

D««(«eeihe  toble),  eo«itfai»ed  by  hfai  for  <ff  J^ 
TO?hSiU»d  been  pwTk«dy  e-i^ 


.;iM»^ 


tBfw*i"''^i'wpm>  ■ 


PBJtIODIOJTr  OF  BUNBPOTB. 


the  ipota  aw  depw«rfoiw 
10  eitatenc6  of  a  cool  con- 
known  to  bo  impoMlblc. 
ire  BO  mostly  by  contrast. 
:  bMkground,  they  would 
the  photometnc  meamire* 
nucleua  beneath  rach  an 

won  become  BMeo«»,^y 
>f  the  photoai*ere.  The 
f  nearly  conatant  daring 
miatitated  hare  aendbly 

theae  and  other  nam 
idUed,  mve  aa  to  the  fact 
otoaphere. 


hut  it  was  independeutl}'  snggeated  aiid  completely  proved 
hy  SoiiwABB. 


fiB  um  Ain^  'iMittl^^ 


■  iid|^t  iwnt  fo  be  ^i^ 
rostanoe;  Kfce  flie  ooear- 
n  the  ^h,  7«i  ^  i«^ 
J  Holnih  SomrAm  of 
I  br  him  for  lortjr jf«M», 
nbwTail6A>««Mli8a%- 


TABLB  or  SOHWABB'a  RBSULT& 


YaAK 

Dajmof 
ObMrratlon. 

Dm  of  no 

N«w  anwiw. 

vSUllMin 

ttMllMMUe 
MmK 

1886 

977 
978 
989 
844 
917 
980 
970 
947 
978 
944 
900 
168 
908 
900 
968 
M8 
807 
819 
881 
889 
814 
976 
978 
988 
808 
808 
817 

8H 

SIS 

m 

894 

m 

848 
889 
8M 

817 
880 
886 
907 
849 
818 
801 

39 

2 

0 

0 

1 

8 

49 

ISO 

190 

18 

0 

0 

0 

0 

8 

10 

64 

148 

111 

98 

1 

0 

0 

0 

9 

0 

9 

9 

88 

146 

196 

09 

0 

0 

0 

0 

8 

9 

4 

98. 
78 
196 
98 

118 

161 

995 

188 

180 

148 

84 

88 

51 

178 

978 

888 

988 

169 

189 

108 

66 

94 

09 

114 

107 

907 

880 

986 

188 

101 

195 

81 

67 

70 

84 

96 

186 

988 

911 

M4 

160 

194 

190 

98 

4S 

95 

101 

• 

8'78 

1897 

11-88 

1888 

11-86 

1899 

14-74 

1880 

19-18 

1881 

19-89 

1888 

1888 

1884 

1885 

1886 

887 
19-84 

1887 

1888 

18-97 
19-74 

1888 

11-06 

1840.. 

0-91 

1841 

7-86 

1849 

1848 

706 
7-10 

1844 

6-61 

1848 

6>18 

1848 

8-61 

1847 

9>86 

1841.. 

11-16 

vm :.......::. 

10-64 

IMO 

10*44 

1881 

'.:8 

lOOt 

1888 

T-06 

1884 

vm 

6-61 
6«41 

vm 

6-86 

iM.      ..4.      . 

6-68 

7.41 

18M 

10'67 

1880 

10-06 

1881 

8-17 

18M 

6-00 

1888 

6-64 

1884 

6-06 

1888 

8*14 

1888 

18fr..,.. 

7*88 
7-06 

1888 

8-10 

■iiMiaiiaiiaiii 


If 


204 


AUTRONOMY. 


The  periudicity  of  tho  spots  is  ovidont  from  tliu  tahlu. 
It  will  appear  in  a  more  striking  way  from  tho  following 
■nmmary : 


FVoa  18W  to  1881,  sun 

without  ipotfl 

on  onljr . . . . 

1  day. 

In  1888, 

M 

ii 

180  d»7B. 

From  1886  to  1840,    " 

4< 

II 

8     " 

In  1848, 

M 

<* 

147     " 

Piom  1847  to  1851     ** 

II 

H 

8     " 

In  1868, 

•1 

«• 

.     198     " 

From  1858  to  1881»    '* 

II 

M 

no  A».y. 

In  1887, 

M 

«l 

.    198  dayi. 

Every  11  years  there  is  a  minimum  number  of  spots, 
and  about  6  years  after  each  niinimum  there  is  a  maxi- 
If  instead  of  merely  counting  the  number  of  spots, 


mum. 


measurements  are  made  on  solar  photograms,   as  they 
are  called,  of  the  extent  of  spotted  otmi,  the  period  comes 
out  with  greater  distinctness.     This  periodicity  of  the 
area  of  the  solar  spots  appears  to  be  connected  with  mag- 
netio  phenomena  on  the  earth's  surface,  and  with  the  num- 
ber of  auroras  visible.     It  has  been  supposed  to  be  con- 
nected also  with  variations  of  temperature,  of  rainfall, 
and  with  other  meteorological  phenomena  such  as  the  mon- 
soons of  the  Indian  Ocean,  etc.     The  cause  of  this  period- 
icity is   as  yet   unknowE.     Oakukotoh,  Db  la  Bus, 
LoBWT,  and  SrswAkr  have  given  reasons  which  go  to  show 
that  there  is  a  connection  between  the  spotted  area  and  the 
configurations  of    the  planets,  particularly  of   Jupiier^ 
VenitSf  and  Mercury.     Zollnkb  says  that  the  cause  lies 
within  the  sun  itseU,  and  assimiktes  it  to  the  periodic 
action  of  a  geyser,  which  seems  to  be  ^  priori  probable. 
Since,  however,  the  periodic  variations  of  the  spots  oor- 
respond  tq  the  magnetic  variation,  as  exhibited  in  the  last 
column  of  the  table  of  Sohwabk'h  results,  it  appears  that 
there  may  be  some  connection  of  an  unknown  nature 
between  Uie  sun  and  the  earth  at  least.     But  at  praient 
wtt  oan  only  state  our  limited  knowledge  and  wait  for 
further  information. 


■awe! 


idont  from  tho  tal>lu. 
y  fruiii  tho  following 


onl/.. 


1  day. 

.    189  dsjri. 

8     " 

.    147     •• 

2     " 

.     198     " 

no  day. 

.     108  daya. 

im  nnml)cr  of  epote, 
luiii  there  is  a  inaxi- 
^  the  number  of  spots, 
photogrsms,   as  they 
rea,  tho  period  comes 
IS  periodicity  of  tho 
connected  with  mag- 
loe,  and  with  the  nnm- 
snpposed  to  be  oon- 
iperatnre,  of  rainfall, 
imena  such  as  the  mon- 
le  cause  of  this  period- 
iNOToir,  De  la  Bue, 
iBons  which  go  to  show 
tie  spotted  area  and  the 
ticnlarly  of   JupUery 
ys  that  the  cause  lies 
tea  it  to  the  periodic 
be  a  priori  probable, 
ions  of  the  spots  oor- 
KB  exhibited  in  the  last 
results,  it  appears  that 
'  an  unknown  nature 
least.    But  at  preaent 
dwledge  and  wait  for 


mmm 


S96 


ABTRONOMT. 


From  the  first  serios  of  earlier  obflervations,  the  period 
comes  ont  from  observed  vfwnvma,  11>20  yean,  with  a 
variatioii  of  two  years  ;  from  observed  maxima  the  period 
is  11 '20  years,  with  variation  of  three  years — ^that  is,  this 
series  shovrs  the  period  to  vary  between  18 '3  and  9>1 
years.  If  we  sappose  these  errors  to  arise  only  from  errors 
of  observation,  and  not  to  be  real  changes  of  the  period 
itself,  the  mean  period  is  11-20  ±  0-64. 

The  results  from  the  second  series  are  also  given  at 
the  foot  of  the  table.  From  a  combination  of  the  two,  it 
follows  that  the  m>ean  period  is  11 -111  ±  0*307  years, 
with  an  oscillation  of  ±  3 -030  years. 

These  resnlts  are  formulated  by  Dr.  Wolv  as  follows : 
The  frequency  of  solar  spots  has  continued  to  change 
periodically  since  their  discovery  in  1610  ;  the  mean  length 
of  the  period  is  11^  years,  and  the  separate  periods  may 
difEer  from  this  mean  period  by  as  mudi  as  2*03  years. 


A  general  reladon  between  the  frequency  of  the  spots  and  the 
Tuiaaon  of  the  magnetie  needle  is  mown  by  the  nombers  which 
have  been  giveu  in  the  table  of  Scbwabb's  resolts.  This  relation 
has  been  most  closely  studied  by  Wour.  He  denotes  by  t  the 
number  of  sronps  of  spots  seen  on  any  day  on  the  sun,  eonntiag 
each  iaolateld  spot  as  a  group ;  br/  is  denoted  the  number  of  spots 
in  each  gmupC^is  then  ptoDornonal  to  the  spotted  area) ;  Iv  i  a 
ooeOdent  depending  upon  the  size  of  the  telescope  used  for  (wser- 
vatiop,  and  by  r  the  oidly  twdrtJM  memlir  so  called ;  th«u  he  snp^ 
poses 

r  =  *  (/+  t^i'ff^ 

From  the  daily  relative  numbers  are  formed  the  meaa  oMithly; 
and  tlw  mean  annual  relative  numbers  r.  Then,  accordiae  to 
Wour,  If  •  is  the  mean  annual  variation  of  the  magnetic  ueeiue  at 
any  plape,  two  omrtaats  for  that  place,  a  and  /a,  can  be  found,  so 
flu*  the  follonrtqg  f ormida  is  true  for  all  years : 

e  =  a  +  /i'r. 

Thus  for  Munich  the  formula  becomes. 


9  =  r-»7  +  V-OBl  r; 


and  lor  Prague, 


TOTAL  BOLIPasa  OF  THB  SUN. 


S97 


lervations,  the  period 
11 '20  yean,  with 
d  maxima  the  period 
le  yean — ^that  is,  this 
tween  ld>3  and  91 
uise  only  from  errors 
unges  of  the  period 

64. 

ies  are  also  given  at 
ination  of  the  two,  it 

111  ±0.307  years, 

r.  WoLT  as  follows : 
continued  to  change 
)10  ;  the  mean  length 
leparate  periods  may 
inch  as  2 '03  years. 

loy  of  th«  ipots  and  the 
D  by  the  nnmberB  which 
'a  reaolta.  This  relation 
\  He  denotes  hy  9  the 
day  on  the  mn,  counting 
died  the  anmber  of  spots 
the  spotted  area) ;  bv  i  a 
teleaoope  used  for  omwr- 
r  so  odied ;  then  he  njf- 


tnned  the  mean  monthly 
r.  Then,  acoordiu;  to 
*f  the  magnetic  aaeue  at 
r  and  A  can  be  fomd,  so 
rears: 


id  so  on. 


TlAB. 

MuMioa. 

PBAAUa. 

ObMmd. 

Compated. 

A 

OtMerrad. 

Compatad. 

& 

1870 

1871 

1878 

1878 

18-27 

11  70 

10-86 

9-18 

18*77 

11. 56 

11-18 

9-84 

-0-50 
+  0-14 
-017 
-0-48 

1141 

11-60 

10-70 

905 

18-10 

10-88 

10-46 

8-87 

-0-68 
+  0-71 
+  084 
+  0-18 

The  above  comparison  bears  out  the  conclusion  that  the 
magnetic  variations  are  subjected  to  the  same  pertorba- 
tions  as  the  development  of  the  solar  spots,  and  it  may 
be  said  that  the  chimges  in  the  frequency  of  solar  spots 
and  the  like  changes  of  magnetic  variations  show  that 
these  two  phmomena  are  dependent  the  one  on  the  other, 
or  rather  upon  the  same  oosmioal  cause.  What  this  cause 
is  remains  as  yet  unknown. 

8  4.    TBDi  BUIPB  COSBOKOtPHMBJI  AHD  OOBOIIfA. 

TbfliioiiMsift  of  Total  JtflipaM. — ^The  beginning  of  a 
total  solar  eclipse  is  an  insignifieant  phenomenon.  It  is 
marked  simply  by  the  small  blaok  notch  made  in  the  lu- 
minous disk  of  t^  sun  by  the  advancing  edge  at  Hmb  of 
the  moon.  This  always  occurs  on  tiie  western  half  of  the 
sun  j  aa  the  moon  moves  from  west  to  east  in  its  ort^  An 
hour  or  more  must  elapse  b^<ne  the  nioon  haa  advanoed 
snffimantly  far  in  its  orbit  to  cover  the  ran's  disk.  Zhuing 
this  time  the  disk  of  the  nm  ia  gradually  hidden  imtil  it 
beounea  a  thin  creaocnt  To  like  genoni  spertator  theie 
is  little  to  aodee  during  the  fint  two  thirds  of  this  period 
fnm  the  beginning  of  the  edUpse,  unlesajt  be  perh^ia  the 
altered  fHavsm  of  the  imagee  formed  by  small  holpi  or 
i^erlnres.  Under  orcUQaiy  ohremMtanoei,  the  image  d! 
thvnu,  m^de  by  the  aolar  caya  whiehpaas  thim^  a  flMll 
hoW-^lii*ei)Bd»£(i««aiiip]fa.--«(» deodar  ia  ih^  Uwlle 
dn|»  of  ^  liii  iiaait    When  tiio  ana  ia  OMaoent,  Hie 


MMMM 


398 


AaTBONOMT. 


image  of  the  eon  formed  by  sach  rays  is  also  crescent, 
and,  under  favorable  circumstanceB,  as  in  a  thick  forest 
where  the  interstices  of  the  leaves  allow  snch  images  to  be 
formed,  the  effect  is  quite  striking.  The  reason  for  this 
phenomenon  is  obvious. 

The  actual  amount  of  the  sun's  light  may  be  diminished 
to  two  thirds  or  three  fourths  of  its  ordinary  amount  with- 
out its  being  strikingly  perceptible  to  the  eye.  What  is 
first  noticed  is  the  chuige  wUch  takes  place  in  the  color 
of  the  surrounding  landscape,  which  begins  to  wear  a  rud- 
dy aspect.  This  grows  more  and  more  pronounced,  and 
gives  to  the  adjacent  country  that  weird  ^ect  which  lends 
so  much  to  the  impressiveness  of  a  total  eclipse.  The  rea- 
son for  the  change  of  color  is  simple.  We  have  already 
said  that  the  sun's  atmosphere  absorbs  a  large  proportion 
of  the  bluer  rays,  and  as  this  absorption  is  dependent  on 
the  thickness  of  the  solar  atmosphere  through  wiueh  the 
rays  must  pass,  it  is  plain  that  just  before  the  sun  is  total- 
ly covered  the  rays  by  which  we  see  it  will  be  redder  than 
ordinary  sunlight,  as  they  are  those  which  come  from 
points  near  the  sun's  limb,  where  they  have  to  pass  throng 
the  greatest  thickness  of  the  sun's  atmosphere. 

The  color  of  the  light  becomes  more  and  more  lurid  up 
to  the  moment  when  the  sun  has  nearly  disappeared.  "U. 
the  spectator  is  upon  the  top  of  a  high  mountain,  he  can 
tiien  begin  to  see  the  moon's  shadow  rushing  toward  him 
at  the  rate  of  a  mile  in  about  two  seconds.  Just  as  the 
riiadow  reaches  him  there  is  a  sadden  increase  tA  darinuMi 
-^e  brighter  stars  begin  to  ddne  in  the  daik  lurid  dcy, 
the  thin  eresoent  of  the  sun  breaks  up  into  anmll  pdnts  w 
dots  of  light,  whidi  suddenly  disiqvptar,  and  the  moon  it- 
self, an  intensely  black  ball,  appewa  tohai^iadat«d  in  tiie 
heavens. 

An  iuBtant  afterward,  the  corona  is  seen  sinToimdbw  tike 
Made  disk  of  tiie  raoim  widi  a  soft  eMgsnee  cp^wkft- 
flttt  from  wy  odwr  Bglit  laio^^Btttas.  IBkm  ik»m^m^% 
UfBb  it  is  liKteMiSy  bfi|^  and  toUw  iMfctd«7» 


— .  iMifciiiaiiniiiiii 


msssBssmsm 


TOTAL  EOLIPSBB  OF  THE  SUN. 


m 


rays  is  also  crescent, 
as  in  a  thick  forest 

ow  snch  images  to  be 
The  reason  for  this 

^ht  maj  be  diminished 
ordinary  amount  with- 
to  the  eye.    What  is 
es  place  in  the  color 
begins  to weara  md- 
lore  jnonounced,  and 
eird  effect  which  lends 
x>tal  eclipse.  Therea- 
We  have  already 
>bs  a  laige  proportion 
ption  is  dependent  on 
re  through  which  the 
}ef  ore  the  sun  is  total- 
)  it  will  be  redder  than 
Nse  which  come  from 
)y  have  to  pass  through 
itaiosphere. 
ore  and  more  lurid  up 
learly  disappeared,     tt 
iSf^  mountain,  he  can 
w  rushing  toward  him 
seconds.    Just  as  tiie 
on  inerease  of  dailniflM 
in  the  daik  lurid  aky, 
up  into  nun  points  er 
p0ar,  and  the  moon  i\r 
I  tohuigisola*«d  in  tibe 

is  seen  twrcnui^^  die 

dMgniee  quite  dUkr* 

na.    S«ir  iw  oMtf^s 

in  nted  «9» 


in  structure ;  5'  or  10'  from  the  limb  this  inner  corona 
has  a  boundary  more  or  less  defined,  and  from  this  extend 
streamers  and  wings  of  fainter  and  more  nebulous  lif^t. 
These  are  of  various  shapes,  sizes,  and  brilliancy.  No 
two  solar  eclipses  yet  obseoved  have  been  alike  vx  this  re> 
spect 

These  wings  seem  to  vary  from  time  to  time,  though  at 
nearly  every  eclipse  the  same  phenomena  are  described  by 
observera  situated  at  different  points  along  the  line  of 
totality.  That  is,  these  appearances,  though  dumgeable, 
do  not  change  in  the  time  the  moon's  shadow  requires  to 
pass  from  Vancouver's  Island  to  Teias,  for  ezamplei  whidi 
is  some  fifty  minutes. 

Superposed  upon  these  wings  may  be  seen  (sometimes 
with  the  naked  eye)  the  red  fitunes  or  protuberances  whioh 
were  fint  discovert  during  a  solar  eclipse.  These  need 
not  be  more  closely  described  here,  as  they  can  now  be 
studied  at  any  time  by  aid  of  the  speotrosoc^)*. 

The  total  phase lastk  for  afew  minutfls  (nevor  more  than 
six  or  seven),  and  during  this  time,  as  the  eye  beoomea  more 
and  more  accustomed  to  the  faint  lights  the  outer  oorona  is 
sem  to  Btretoh  furi&er  and  fnrtliMr  away  fnna  th*  «aii'« 
limb.  At  the  «eHpBe  of  1878,  July  2Mi,  it  was  «em  by 
Prdeaor  Lavouet,  and  by  one  of  the  writen,  to  eortend 
noie  than  6**  (lAxNit  9,000,000  miles)  from  4iba  son's  Mb. 
Just  b^fera  ^  end  of  the  total  pinae  flwre  is  a  raddm 
inawaia  <rf  the  brightwas  qf  tbealy,  due  to  the  iaayaiid 
ilhudBation  «f  ilM  «M43i*t  atuwaphwe  near  tiie  'ofaMrvw, 
and  in  a  momMit  men  ^  sim^a  nja  are  again  viASe, 
mmOa^mh^ii^mmm.  IbmntiieeBdef telaMfytfll 
liielMkeMrtaaltfieylMMNDMna  ef  the  fiat  Utt  «<  tfie 
esBpae  aw  wpeatod  in  iuy— e  esdir.     ^ 

"    '  ue  «!► 


mm 


m 


800 


ABTBONOMT. 


ter  are  sometimes  seen  to  be  almost  totally  black.  The 
appearances  are  extremely  irregular,  but  they  are  often  as 
if  the  inner  corona  were  made  up  of  brushes  of  light  on  a 
darker  baokground.  The  direction  of  these  brushes  is 
often  radial  to  the  sun,  especially  about  the  poles,  but 
where  the  outer  corona  joins  on  to  the  inner  these  brushes 
are  sometimes  bent  over  so  as  to  join,  as  it  were,  the 
boundaries  of  the  outer  light. 

The  great  difSculties  in  the  way  of  studying  the  corona 
have  been  due  to  the  short  time  at  the  diqrasal  of  the  ob- 
server, and  to  the  great  differences  whi(^  even  the  best 
drau^tsmen  will  make  in  their  rapid  sketches  of  so  com- 
plicated a  phenomenon.  The  figure  of  the  inner  corona 
(m  l^e  next  page  is  a  copy  of  one  of  the  best  drawings  made 
of  the  eclipse  of  1869,  and  is  inserted  chiefly  to  show  the 
nature  of  the  only  drawings  possible  in  the  limited  lime. 
The  numbers  refer  to  the  red  prominences  around  the  Emb . 
The  radial  structure  of  the  corona  and  its  different  ezten- 
tton  and  nature  at  different  points  are  also  indicated  in  the 
drawing. 

The  fifpin  <m  page  802,  Is  Mopy  of  a  envoa  drawing  inade  in  1878. 
verldeiiee  whieh  w«  cm  gain  of  the  detdls  of  tlM«« 


nubeet 

oookes,  however,  f  mni  a  eetiae  of  photognqriu  taken  daring  the  whole 
of  totality.  A  photoglyph  with  a  ihort  expoeure  f^ves  the  detaik 
of  aie  inner  ooiona  wdl,  bat  it  not  dbeted  Iqr  the  fidnter  ootlving 
parte.  One  of  loiuni  ezpoenre  shows  details  inrilisr  away  ham 
ttesoB'sUnb,  wh&  thoee  near  it  are  lost  hi  a  riam  of  light,  hifaw 
«ver-«zpowd,  and  so  on.  In  this  w4y  a  aenes  of  phofcMinplis 
fAnm  OS  the  neaas  iA  hidldfaig  op,  as  it  Were,  llie  whoHi  eMona 
fiwB  Us  hrii^iteak  parts  near  tiMaan'slisril>  onttothefsiBlsskpa*- 
tiaas  wUdi  will  hnpnss  thaaMshpes  on  a  photagiaplde  ph4a. 

Tln6  oorona  and  rod  promiBiraoeB  aro  aolar  appoidagea. 
It  was  lonneriy  donfatfol  whetbar  :>th«  omnia  w«  an 
atmosphere  belonging  te  the  auner  to  the  9M0B.  <At^ 
eoU^  of  1860  it  wan  piwved  hjmmmnmiBm  tilil  tiw 
mA  fttm&moom beli»|(ed  to  the  im  wid  Mlti^lhtiipoB, 

tiM  mam  gnMB^  ooiw«d  thaiift  bg^^  i^^ 
^Mr  wuMiiiriiiiC-ittadiBd  to  tiwirm     Tpht  i 


iiiiiittillili 


totally  black.  The 
but  they  are  often  as 
bnuhee  of  light  on  a 

of  these  bnuhea  is 
abont  the  poles,  but 
le  inner  these  bnuhes 
join,  as  ii  were,  the 

I  studying  the  corona 
be  dii^KMal  of  the  ob- 

whioh  even  the  best 
d  sketches  of  so  com- 
)  of  the  inner  oorona 
lie  best  drawings  made 
id  chiefly  to  show  the 

in  the  limited  time. 
)nces  aronnd  the  Bmb . 
nd  its.  different  exten- 
n  also  indioated  in  the 


roa  drawing  mafle  la  1878. 

the  detdk  of  'tlM«oiona 
ihs  taken  dofinif  tlie  wliole 
izpoMin  ghrw  the  aetalk 
ed  hy  the  Mater  ootMog 
etaite  farther  away  mm 
t  in  a  olan  of  U|^  hriag 

a  eem  of  iihotamphe 
b  wen,  the  n^^lMom 
lb  ont  to  the  frinlest  pov- 


I  tm  aqlir  appidagcs. 
r  'the  owona  mm  an 
toihftinooii.  i  At  the 
mmmwffnwnti  ^IbAl  ihe 


THE  SUJTS  PBOMnfENOBB. 


808 


mm.  There  were  others  of  varions  and  perhaps  varying 
shapes,  and  the  haaes  of  these  were  oonneoted  hy  a  low 
band  of  serrated  rose-colored  light.  One  of  theM  protn- 
berances  was  shown  to  be  entirely  above  the  sun,  aa  if 
floating  within  its  atmosphere.  Around  the  whole  disk 
of  the  sun  a  ring  of  similar  nature  to  the  prominenoee 
exists,  whieh  is  brighter  than  the  corona,  and  seems  to 
form  a  base  for  the  protnbenmoea  theniBelves ;  this  is 
the  sierra.  Some  of  the  red  flames  were  of  enormous 
height ;  000  of  at  least  80,000  miles. 


(l«68j  l«|r)^nM  totil  in  Ind{%  loaiiii  tilMeiNn^ 

▲  4inoff«7  of  iLiiMniHi'^irffl 

and  ty  ft  eVi<>i  wnjf^m  |wif ii|«inMi 
iihB^lnlthir -irta'  ifrj*  Vait-  tfw.  iutfi'ii&fn 

WM  iBOeCt  v^Mii.  1^  lii'';^<SOiBiP'-WWiieii* 

1^  hri^  linni  ^  IgribwgW  1^ 

*1iimrVllt0imMmimkimmtnmHfi*'i^^  BMT  Finis. 


■Ml 


mm 


804 


A8TR0N0MT. 


' 


The  brightnoM  of  the  spectrnm  was  so  marked  that 
Janbsen  detenninod  to  keep  his  spectroscope  fixed  upon  it 
even  after  the  reappearance  of  snnlight,  to  see  how  long  it 
could  be  followed.  It  was  found  that  its  spectrum  could 
still  be  seen  after  the  return  of  complete  sunlight ;  and  not 
only  on  that  day,  but  on  subsequent  days,  similar  phenom- 
ena could  be  obiserved. 

One  great  difficulty  was  conquered  in  an  instant.  The 
red  flames  which  formerly  were  only  to  be  seen  for  a  few 
moments  during  the  comparatively  rare  occurrences  of 
total  eclipses,  and  whose  observation  demanded  long  and 
expensive  journeys  to  distant  parts  of  the  world,  could 
now  be  regularly  observed  with  all  the  facilities  offeied  by 
a  fixed  observatory. 

This  great  step  in  advance  was  independently  made  by 
lb.  Lotnnrn,*  and  his  discovery  was  derived  from  pure 
theory,  unaided  b/  the  eclipse  itself.  By  this  method 
the  prominences  have  been  carefully  mapped  day  by 
day  an  around  the  tnn,  and  it  has  been  proved  that 
anrand  this  body  there  is  a  vast  atmosphere  of  hydn^;en 
gas — the  (Arwrniotphere  or  titrra.  From  out  of  this  the 
praninenoes  are  projected  imnetimes  to  hei^^ts  of  100,000 
kiknpietru  w  more. 

It  win  bq  neoeMuy  to  recall  Um  main  faeto  of  obaarvatkm  which  an 
ftuidaiMatal  in  tiM  1U8  of  Um  qwdnaoope.  WhanaWlUantpalatb 
examiiMd  with  the  spectroeoope.  It  ia  q;n«ad  oat  by  tin  priam  hito  a 
band-^he  apactmiii.  Dringtwopcianu,  thaqtectnuBlwoaiiHalaa«Br, 
bat  the  li^t  of  the  aarfaoe,  beiac  ipnad  over  a  neater  ana,  ia  en- 
feebled. Thne,foar,  ormove  pnana  ipmad pat tte speetrem  propor- 
tionally  mora.  If  the  lyeotwim  ia  of  ahlacandeacentaoiidorliqaw,  it 
iaalwaya  omtinuoaa,  and  it  can  be  eofealiled  to  any  dagne ;  ao  that 
any  part  of  it  can  be  made  aa  feeble  aa  deaired. 

TTOBMthodfapndaelyaimBarfanrinfltelatotheBaeofthetelaaaipe 
In  viewing  ataia  in  the  daytinM.  The  tefcuffipe  loaMm  the  brBHawqr 
of  the  aky,  while  the  dlA  of  the  atar  la  kSpt  ctf  the  aaawdnlenity, 
aa  it  la  a  pdnt  in  itadf  .  ItthuabaeoneavUbla.  If  It'^ajdiiwbiffgaa, 
ita  apaetram  trill  oonaiat  of  a  dell&ito  nomberof  Uaea,  aav  nine-^,  B. 
O.foreiainiile.  Kow  aajgywe  the apeetrom of ttii  gaa  tojn  aMpaipnaed 
OB  the  eonliuMNia  apectrnm  of  the  son;  bgriMiBf  onlyoae  pmaa,^ 


*  Mr.  J.  NoBiua  Looam,  F.R.8.,  of 
the  Bdenoe  and  Art  Department  ^  the  Sooth  K« 


MM 


TUB  SUIT  a  UKAT. 


300 


was  80  marked  that 
stroBcope  fixed  upon  it 
ght,  to  see  Itow  long  it 
lat  its  spectrnm  could 
>lete  sunlight ;  and  not 
days,  similar  phenom- 

d  in  an  instant.  The 
y  to  be  seen  for  a  few 
r  rare  occurrences  of 
1  demanded  long  and 
«  of  the  world,  conld 
the  f adlitieB  offered  by 

ndependently  made  by 
as  derived  from  pure 
)elf .  By  this  method 
'nlly  mapped  day  by 
has  bem  proved  that 
noaphere  of  hydrogen 
From  out  of  thk  the 
»to  heights  of  100,000 


sU  of  obMnration  which  an 
«.  WhaaabfOUantpoiatia 
•d  oat  ti7  flie  primi  faito  a 
iMspeotmmbeoaiiMS  longBT, 
o««r  a  neater  ana,  is  ea- 
■d  oat  the  qieelrani  propor- 
oaadesoent  solid  or  liquid,  it 
lied  to  anjdsgiee;  so  that 
lied.  ^'^ 
;ile  to  the  we  of  flw  tdMoope 
anwpe  iDwui  the  traBaacy 
kSptof  the  saaMttateailtr. 
libk  IfU%a|dswfa«gM, 
berotUaes,  anr  fluee— A,  B. 
of  Ote  BM  taVi  aopeipoied 
roataff  ooifOM  priHt,tke 


ithK< 


Bolar  qwctrum  is  abort  and  briUiant.  and  t  -erypart  of  it  may  be  more 
brilliant  than  tlw  line  spectrum  of  the  gh  ly  incieaaing  tne  disper- 
sion (the  number  of  prisms),  the  sohu-  spt;^  am  is  proportionately  en- 
feebled. If  tlM  ratio  of  the  light  of  the  bodiee  theoMelTes,  tlie  sun  and 
the  gas,  is  not  too  groat,  the  continuous  spectrum  may  be  so  enfeebled 
that  tlM  IfaHs  spectrum  will  lie  Tislble  wnen  superposed  upon  it,  and 
the  spectrum  of  the  gas  may  then  Im  seen  even  in  tne  presence  of  true 
sunlight.  Such  was  the  process  Imagined  and  successfully  carried  out 
by  itr.  LooKTBB,  and  such  is  in  essence  the  metlwd  of  viewing  the 
prominences  to-day  adopted. 

The  Ooroiialllpaotnun.— In  1880  (August  7th)  a  total  aolur 
ecliiwe  was  Tisible  in  the  United  States.  It  was  probiably  otMerved 
by  more  astronomers  tlian  any  preceding  eclipoe.  Two  American 
astronomers,  Professor  Totme,  of  Dartmouth  Oollcne,  and  Professor 
HAREHasa,  of  the  Naval  Observatory,  especially  observed  the  spec- 
trum of  die  corona.  This  spectrum  was  found  to  consist  of  one 
fabt  greoiish  line  croHsing  a  faint  oontinoooa  spectrum.     The 

6 lace  of  this  line  in  the  mi^  of  the  solar  spectrum  published  by 
[iROBHoiPr  waa  occupied  by  a  line  which  he  had  attributed  to  the 
tnm  spectrum,  and  which  had  been  numbered  1474  in  his  list,  so 
that  it  is  now  spoken  of  aa  1474  K.  This  line  is  probably  due  to 
some  jgas  which  must  be  present  in  large  and  possibly  variable 
quantities  in  the  corona,  and  which  is  not  Known  to  us  on  the  earth, 
in  this  form  at  least.  It  is  probably  a  sas  even  lifter  than  hydro* 
gen,  aa  the  existence  of  this  line  has  been  traced  10'  or  SO'  fhaa 
the  snn*s  limb  nearly  all  aroand  the  disk. 

In  the  eclipse  of  JulySMh,  1878,  which  was  total  in  Colorado 
and  Texas,  the  omi^aoaa  spectrom  of  the  corona  waa  found  to  be 
crossed  by  the  dark  lines  of  the  solar  roectrum,  showing  that  the 
coronal  light  was  composed  in  part  of  reflected  sunlight. 


%  6.    SOUBOm  OT  TBM  SUITS  HSAT. 

Thaoriaa  of  tba  8nn*a  Oooftitatioii.  —  No  considerable 
fraction  of  the  heat  radiated  from  the  sun  returns  to  it 
from  the  celestial  spaces,  since  if  it  did  the  earth  would 
intercept  some  of  ue  returning  rays,  and  the  temperature 
of  night  would  be  more  like^that  of  noonday.  But  we 
know  the  ran  i»  daily  radiating  into  space  2,170,000,000 
timea  as  muc3i  heat  aa  is  daily  received  by  the  earth,  and 
it  follows  that  unleM  the  supply  of  heafu  infinite  (which 
ire  cannot  believe),  this  enormous  daily  radiati<m  murt  in 
time  exhanat  the  ra^y.  Wh«i  the  supply  is  exhausted, 
or  even  8erk>u8ly  trenched  upon,  the  result  to  the  inhab- 
itants of  the  earth  will  be  fatal    A  slow  diminnUon  of 


806 


ABTRONOMV. 


H 


the  daily  snpplj  of  heat  would  prodnce  a  slow  change  of 
climates  from  hotter  toward  colder.  The  Berions  results 
of  a  fall  of  60°  in  the  mean  annual  temperature  of  the 
earth  will  be  evident  when  we  remember  that  such  a  fall 
would  change  the  climate  of  France  to  that  of  Spitzber- 
gen.  The  temperature  of  tlie  sun  cannot  he  kept  up  by 
the  mere  combustion  of  its  materials.  If  the  sun  were 
solid  carbon,  and  if  a  constant  and  adequate  supply  of 
oxygen  were  also  present,  it  has  been  shown  tliat,  at  the 
present  rate  of  radiation,  the  heat  arising  from  the  com- 
bustion of  the  mass  would  not  last  more  than  6000  yean. 

An  explanation  of  the  solar  heat  and  light  has  been 
suggested,  which  depends  upon  the  fact  that  great  amounts 
of  heat  and  light  are  produced  by  the  collision  of  two 
rapidly  moving  heavy  bodies,  or  even  by  the  passage  of 
a  heavy  body  like  h  meteorite  through  the  earth's  atmos- 
phere. In  faet,  it  we  had  a  certain  mass  availalle  with 
which  to  producb  heat  in  the  sun,  and  if  this  mass  were  of 
the  best  possible  materials  to  produce  heat  by  burning, 
it  can  be  shown  that,  by  bnming  it  at  the  surface  of  tbs 
sun,  we  should  produce  vastly  less  heat  than  if  we  simply 
allowed  it  to  fall  into  the  sun.  In  the  last  case,  if  it  fell 
from  the  earth's  dirtuice,  it  would  give  6000  times  more 
heat  than  by  its  buniing. 

I'ii^  Uati  velocity  with  which  a  body  from  space  oonld 
fall  dpon  the  sun's  surfaoe  is  in  the  ndghborhood  of  280 
miles  in  a  second  of  time,  and  the  velodly  may  be  as  great 
as  860  miles.  From  these  facts,  tiie  meteoric  theory  of 
solar  heat  originated.  It  is  in  effect  that  the  heat  of  ^ 
•nn  is  kept  up  by  the  impact  of  meteors  up<m  its  surfaoe. 

Ko  doubt  immense  numben  of  meteorites  fall  into  the 
sun  daily  and  hourly,  and  to  each  one  of  them  a  certain 
considerable  portion  of  heat  is  due.  It  is  found  that,  to 
account  for  the  present  amount  of  radiati<m,  meteorites 
equal  in  mass  to  tiie  whole  earth  would  hare  to  fall  into 
the  mm  every  cMitury.  It  is  extxemely  haprobthle  that  a 
mass  one  tenth  as  lai^  as  this  is  added  to  ^e  sun  in  this 


SUPPLY  OF  80LAU   HEA1\ 


nee  a  slow  change  of 
The  Berions  resultfi 
temperature  of  the 
lembertliat  snch  a  fall 
to  that  of  Spitzber- 
cannot  be  kept  np  by 
als.    If  the  sun  were 
ado(]nate  supply  of 
ten  shown  that,  at  the 
arising  from  the  com- 
Tiore  than  5000  yeans. 
It  and  light  has  been 
act  that  great  amounts 
|r  the  collision  of  two 
ven  by  the  passage  of 
gh  the  earth's  atmos- 
n  mass  availal!e  with 
nd  if  this  mass  were  of 
noe  heat  by  burning, 
t  at  the  surface  of  the 
leat  than  if  we  simply 
the  Uwt  case,  if  it  fell 
give  6000  times  more 

body  from  space  could 
)  neighborhood  of  880 
elocil^  may  be  as  great 
he  meteorio  theory  of 
t  that  the  heat  of  the 
eora  upmi  its  snrfaoe. 
leteoritea  itSi  into  the 
ne  of  them  a  oertain 
It  is  found  that,  to 
f  radiation,  meteoritea 
trald  hare  to  fall  into 
lely  improbable  that  a 
led  to  the  sun  in  thia 


way  per  century,  if  for  no  other  reason  because  flx'  tt^  .t 
itself  and  every  planet  would  receive  far  more  tliai*  m 
present  share  of  meteorites,  and  would  itself  become  (|i»i  *< 
hot  from  this  cause  alone. 

There  is  still  another  way  of  accounting  for  the  sun-s 
constant  supply  of  energy,  and  this  has  the  advantage  of 
appealing  to  no  cause  outside  of  the  sun  itself  in  tlie  ex- 
planation. It  is  by  supposing  the  heat,  light,  etc. ,  to  be 
generated  by  a  constant  and  gradual  contraction  of  tlie 
dimensions  of  the  solar  sphere.  As  the  globe  cools  by 
radiation  into  space,  it  must  contract.  In  so  contracting  its 
ultimate  constituent  parts  are  dravm  nearer  together  by 
their  mutual  attraction,  whereby  a  form  of  energy  is  de- 
veloped which  can  be  transformed  into  heat,  light,  elec- 
tricity, or  other  physical  forces. 

This  theory  is  in  complete  agreement  with  the  known 
laws  of  force.  It  also  admits  of  precise  comparison  with 
facts,  since  the  laws  of  heat  enable  us,  from  the  known 
amount  of  heat  radiated,  to  infer  the  exact  amount  of  con- 
traction in  inches  which  the  linear  dimensions  of  the  sun 
must  undergo  in  order  that  this  supply  of  heat  may  be 
kept  unchanged,  as  it  is  practically  found  to  be.  With 
the  present  sixe  of  the  sun,  it  is  found  that  it  is  only 
necessary  to  suppose  that  its  diameter  is  diminishing  at  the 
rate  of  about  390  feet  per  year,  or  4  miles  per  century, 
in  order  that  the  supply  of  heat  radiated  shall  be  constant. 
It  is  plain  that  snch  a  change  as  this  nuty  be  taking  place, 
since  we  possess  no  instrmnento  suffldently  delicate  to 
have  deteoted  a  ohimge  of  even  ten  times  this  amount 
since  the  invention  of  the  telescope. 

It  may  seem  a  pandoxical  oonclnsion  that  the  cooling 
of  a  body  may  cause  it  to  become  hotter.  This  indeed  is 
true  only  when  we  sappoae  the  interior  t<Fbe  gaseous,  and 
not  solid  or  liquid.  It  is,  however,  proved  by  theory  that 
this  law  holds  for  gaseous  masses. 

If  a  iplierical  mais  of  gas  be  eondenfwd  to  om  half  ths  prindtiTe 
'  r,ttieoentimlattne(ioiiapi»say  partofitsuMHswUlbfliB* 


mmi 


.'J08 


ASTRONOMY. 


croMed  fourfold,  while  tho  turfMO  ■iibjoctod  to  this  attraction  will 
lie  reduced  to  one  fourth.  Hence  the  preMure  per  unit  of  surfm  i> 
will  be  ftugmeuted  aiiteen  time*,  while  the  deniltv  will  be  incrcMed 
but  elttht  time*.  If  the  elutic  and  the  gnivitkting  forces  w«ri>  in 
equilibHtim  in  the  original  condition  of  the  omm,  tho  tempemturu 
muet  be  «loublod  in  ordtr  that  thov  aiay  itiU  be  in  equilibrium  when 
tho  diameter  ia  reduced  to  one  half. 

If,  howerer,  the  primitire  Ixidy  ia  originally  aolid  or  liquid,  or  iif, 
in  the  oounw  of  time,  it  liecomes  so,  then  thia  law  c«aaea  to  hold,  and 
radiation  of  heat  produces  u  lotroring  of  the  temperature  of  tho 
body,  which  progressively  continues  until  It  ia  flually  reduced  to  tho 
temperature  of  sunoundfng  space. 


We  cannot  say  whether  the  snn  hiu  yet  begnn  to  liqnofy 
in  his  interior  parts,  and  hvnco  it  is  impoisible  to  predict 
at  present  the  dnratiou  of  his  constant  radiation.  Theory 
shows  us  that  after  about  6,000,00U  years,  the  sun  radiating 
lieat  as  at  present,  and  still  remaining  gaseous,  will  be  re- 
duced to  one  half  of  its  present  volume.  It  seems  prob- 
able that  somewhere  about  this  time  tlie  solidification 
will  have  begun,  and  it  is  roughly  estimated,  from  this 
line  of  ai^^ment,  that  the  present  conditions  of  heat  radi- 
ation cannot  last  greatly  over  10,000,000  yean. 

The  future  of  the  sun  (and  hence  of  the  earth)  cannot, 
as  we  see,  be  traced  with  great  ex-\otitude.  The  past  can 
be  more  closely  followed  if  we  assume  (which  is  tolerably 
safe)  that  the  sun  up  to  the  prnent  has  been  a  gaseous,  uid 
not  a  solid  or  liquid  mass.  Four  hundred  yean  ago, 
then,  the^un  was  about  100  miles  greater  in  diameter 
than  noy^  and  if  we  suppose  this  process  of  contrac- 
tion to  have  regularly  gone  on  at  the  same  rate  (an 
uncertain  supposition),  we  can  fix  a  date  when  tho  son 
filled  any  given  space,  out  even  to  the  orbit  of  Nep- 
ttMM— that  is,  to  the  time  when  the  solar  system  consisted 
of  but  one  body,  and  that  a  giieous  or  nebulous  one. 
It  wfll  subsequently  be  seen  that  the  ideas  here  reached 
dpotikriori  have  a  striking  anal<^  to  the  li  priori  ideas 
of  Kant  and  La  Plaor. 

It  is  not  to  be  taken  for  grantMl,  however,  that  the 
amount  of  heat  to  be  derived  from  th«  oontraotion  of  the 


-^nMM 


ictod  to  this  attraction  will 
»reMure  per  unit  of  siirfiK  c 
hedenritV  will  bo  incruiMed 
gravitating  forces  were  in 
the  mnat,  the  temperuturu 
■till  be  in  equilibrium  when 

(inally  Mlid  or  liquid,  or   f, 
thi>  law  ceases  to  hold,  and 
of  the  temperature  of  the 
1  it  is  finally  reduced  to  the 


hm  yet  begnn  to  liquefy 
is  impoflsiblo  to  prodict 
itant  radiation.  Theory 
0  yean,  the  sua  radiating 
ling  gaseous,  will  be  re- 
rolnme.  It  seems  prob- 
tiine  the  solidification 
hly  estimated,  from  this 
t  conditions  of  heat  radi* 
D00,000  years, 
loe  of  the  earth)  cannot, 
xvstitude.  The  past  can 
Mume  (which  is  tolerably 
it  has  been  agaaeous,  and 
mr  hundred  yean  ago, 
lies  greater  in  diameter 
this  procesB  of  oontrao* 
a  at  the  same  rate  (an 
ix  a  date  when  the  sun 
in  to  the  orbit  oX  Ifejr- 
he  soUur  system  conusted 
laeous  or  nebulous  one. 
i  the  ideas  here  readied 
gy  to  the  <i  priori  ideas 

ited,  however,  that  the 
in  th«  oontraetion  of  the 


AOH  OF  TllK  BUN. 


800 


Hiin'H  diinonftionR  is  infinite,  no  matter  how  liirgo  tho  prim- 
itivtt  tJiiiiiiiiMuim  iiiiiy  hiivu  Im^uii.  A  Innly  fuiliii|f  from 
,iiiy  (liHtunru  tu  the  huh  can  4»iily  liuvu  » (;urtnln  fiiiito  vulm*- 
i -y  deptuiding  un  this  diHtuncu  niid  the  iriiUM  uf  tho  sun 
ilHolf,  which,  even  if  tho  fall  bo  from  nn  infinite  distance, 
nmnot  exceed,  for  tlio  sun,  850  miles  (icr  second.  In 
tho  same  way  the  amount  of  hcnt  generated  by  tho  con- 
traction of  tho  sun's  volume  from  uny  size  to  any  other  is 
finite,  and  not  infinite. 

It  has  been  shown  that  if  the  sun  has  always  l>eei) 
radiating  lieat  at  its  present  rate,  and  if  it  had  originally 
fille<l  all  space,  it  has  required  18,000,000  yean  to  contract 
to  its  present  volume.  In  other  words,  assuming  tlie  pres* 
ont  rate  of  radiation,  and  taking  the  most  favorable  case, 
the  ago  of  the  sun  does  not  exceed  18,000,000  yean.  The  '^ 
earth,  is  of  course,  less  aged.  The  supposition  lying  at  the 
base  of  this  estimate  is  that  the  radiation  of  t)io  sun  has 
)>oen  constant  thronghout  the  whole  period.  This  is  quite 
unlikely,  and  any  changes  in  this  datum  affeot  g^atly  the 
final  number  of  ycara  which  we  have  assigned.  While 
this  number  may  be  greatly  in  error,  yet  the  mothod  of 
obtaitiing  it  Mems,  in  the  present  state  of  science,  to  be 
satisfactory,  and  the  main  c^gdnsion  remains  that  the  past 
of  the  sun  is  finite,  and  that  ■jiLsrobability  its  future  is 
a  limited  one.  The  exact  nui^^^H|||hitariee  that  it  is  to 
last  are  of  no  moment  even  we^^R^Mta  at  hand  to  ob- 
tain them  :  the  essential  point  is,  that,  so  far  as  we  can 
see,  the  sun,  and  incidentally  tho  solar  system,  has  a  finite 
past  and  a  limited  fntnre,  and  that,  lile  other  natural  ob- 
jects, it  passes  through  its  regular  stagM  of  birth,  vigor, 
decay,  and  death,  in  one  order  of  progress. 

^1 }    J  ^  ,  t  yit     ^    i      -^ 


I 


teammm 


,,.xr\Ujc 


(^.^AO^i-P/vMrvc 


3 

r^'^^ 
(^^ 


^fcC^ 


A. 


tJtoE 


Wwv^XifC^'^    \../Qjif<\.  c^yf*^^ 


CHAPTER   III. 

THE  INFERIOR  PLANETS. 

g  1.    MOTIONS  AND  A8FSCT8. 

Thk  inferior  planets  are  those  whose  orbits  lie  between 
tlie  shn  and  the  orbit  of  the  earth.  Commencing  with  the 
more  distant  ones,  they  comprise  VemUy  Mereuryj  and,  in 
the  opinion  of  some  astronomers,  a  planet  called  Vulean^ 
or  a  group  of  plaaets,  inside  the  orbit  of  Mercury.  The 
planets  Mercury  and  Venus  have  so  much  in  common  that 
a  krge  part  of  what  we  have  to  say  of  one  can  be  applied 
to  the  other  wiUi  but  little  modification. 

The  real  and  apparent  motions  of  these  planets  have 
already  been  briefly  deeoribe|^  Part  I. ,  GhapterJY.     It 


will  be  remembered  t 
third  law,  their 
less  than  that  of 
the  latter  betw 
The  interval  between 


irdance  with  Eeplkb's  n 
ition  around  the  Gun  are 
iquently  they  overtake 
tfeiior  conjunctions. 
iDonJTUietions  is  about  four 


vtaidSttB  in  the  case  ol  Jf^noMry,  and  between  nineteen  and 
twwity  months  in  that  of  Vm^9.  At  tl»  end  of  this 
period  eadh  repeKts  the  Moie  series  of  motions  rebtive  to 
the  sun.  What  th«M  notkms  vm  can  be  readily  seen  by 
studying  fig.  84.  In.  &e  first  pkoe,  mippose  the  eurth, 
at  any  point,  E^  of  its  <wbit,  and  if  we  draw  a  line,  S  L 
or  EM,  from  E,  tangent  to  the  orbit  of  dther  ci  these 
j^ets,  it  is  evident  that  the  angle  which  ^ut  line  mdJKMi 
with  that  drawn  to  the  sun  is  the  groateat  dbngatioB  <tf 
the  pUiMt  from  the  wpn.    The  orbits  being  eeoenteie,  tiib 


A8PB0T8  OF  MBROURT  AND  VENUS. 


311 


III. 
LANBT8. 

ASFBOTS. 

hose  orbits  lie  between 
Commencing  with  the 
^ewus,  Meveury^  and,  in 
I  planet  called  Yulcany 
»rbit  of  Mercwry.  The 
10  much  in  common  that 
jr  of  one  can  be  applied 
ation. 

of  these  planets  have 
'art  I.,  Chapter  IV.  It 
>rdance  witii  Kbplbc's 
ion  aronnd  the  sun  are 
equently  they  overtake 
ior  conjunctions, 
junctions  is  about  four 
d  between  nfaieteen  and 
r.  At  the  end  of  this 
3jB  of  motions  reliMiTe  to 
9  can  be  readily  seen  by 
lace,  mippose  the  evrth, 
if  we  draw  a  line,  M  L 
orbit  of  dther  <4  tiM«9 
le  which  1^  line  mdbes 
E)  greatest  doi^pitfaNi  of 
^its  bdng  eeoeiitiio,  t^ 


elongation  varies  with  the  position  of  the  earth.  In  the 
case  of  Mercury  it  ranges  from  16°  to  29",  while  in  the 
case  of  VenuSf  tlie  orbit  of  which  is  nearly  circular,  it 

varies  very  little  from 
45°.  These  planets, 
therefore,  seem  to  have 
an  oscillating  motion, 
first  swinging  toward  the 
Mst  of  the  sun,  and  then 
toward  the  west  of  it,  as 
already  explained  in  Part 
I.,  Chapter  lY.  Since, 
owing  to  the  annual  revo- 
lution of  the  eartL^  the 
■on  has  a  etHiataiit  east- 
wwd  BOKytictti  aimflfig  the 
staiB^  tlMse  pluMii  must 
have,  on  ^  whole,  s  edfreiqpandhig  thom^  inlsniiittent 
motion  fai  the  same  direetion.  Therrfere  Hw  aneient 
astronomers  supposed  their  period  of  fevolation  to  be  one 
year,  the  suae  as  thi^  of  tlw  sun. 

If,  afpubiy  we  draw  a  line  JSSCfnm  the  e«r&  liirougfa 
the  sun,  it  is  evident  that  the  first  point  /,  in  which  this 
line  cuts  the  orbit  of  th^  planet,  or  the  point  of  inferior 
conjunction,  will  (leaving  eccentricity  out  of  the  question) 
be  tiie  least  distance  of  the  planet  from  the  earth,  n^tflethe 
second  point  (7,  ot  the  point  of 
superior  conjunction,  on  the  op- 
posite  side  of  the  sun,  will  be 
the  greatest  distance.  Owing  to 
the  differaioe  of  these  cfotaaoes, 
the  appuent  nagmtnde  of  these 
I^Miets,  as  seen  from  the  earth, 
is  subject  to  great  varfi^om. 

Fig.  dfi  shows  these  vwriatiom  in  the  ease  of  Mereurji^ 
A  r^raMttting  its  iqppMmitini^j^tiidd  when  at  its  graatetl 
^BlMee,  M  lAtm  al  its  mean  dktenw^  «id  C  wlMn  at  fts 


312 


A8TB0N0MT. 


m 


least  diBtance.  In  the  case  of  Venus  (Fig.  86)  the  varia- 
tions are  inndi  greater  than  in  that  of  Mereury,  the  great- 
est distance,  1-72,  lieing  more  tlian  six  times  the  least 
distance,  which  is  only  0  •  28.  The  variations  of  apparent 
magnitude  are  therefore  great  in  the  same  proportion. 

In  thns  representing  the  apparent  angular  magnitude 
of  these  planets,  we  suppose  their  whole  disks  to  he  visible, 
as  they  would  be  if  they  shone  by  their  own  light.  But 
since  they  can  be  seen  only  by  the  reflected  light  of  the 
sun,  only  those  portions  of  the  disk  can  be  seen  which  axe 
at  the  same  time  visible  from  the  sun  and  from  the  earth. 
A  very  little  consideration  will  show  that  the  pn^pmrtion 
of  the  disk  which  can  be  seen  constantily  diminiBheB  as  the 
planet  approaches  the  earth,  fnd  kxdn  laiger. 


'.— An*AsnT  mmmitOum  ov  Dm  <w  vBAn. 


When  the  planet  is  at  its  greatest  dwtanoe,  or  in  superior 
oonjnnction  {jC\  Fig.  84),  its  whole  iUumiiutked  l»Haiii|>here 
can  be  seen  from  the  earth.  As  It  moves  wtwoii  and  ap- 
ftsmSam  dM«wtii,  diftiUiimiiuitedhcnEaspbfflnisgraduaUy 
litfMMlfrMttw.  Ai  tile  point  of  greatest  «lon^on,  Jf 
or  JC^  cme  failf  Ibi  Iwnisphere  is^bie,  and  iL>  f^saet 
Ihmi  ^  ImMi  «£  tf»  pMon  at  fint  os  second  ^mirtsr.  As 
ft  ^gf9mimki»Mm  «m]'nncti<Mi,  tlie  wppumli  visibled&dc 
assumes  the  form  of  a  ovpsoent,  whieh  beeomes  thiayBer 
and  Uiinner  as  tke  ^MMt  appiOieim  tipe  suL 

f%.  87  shows  the  appnraBt  c^k  of  JGpoNry  at  yaiiww 
j^Koes  during  its  iqmodie  vevoliition.  The  plplsl  iiM  ta^ 
pMT  br^ihtest  wh«n  ty»  disk  has  the  fvsttMt  m^bm^ 


wmm 


ASPECTS  OF  MBROUUT  AND  VENUS. 


813 


ms  (Fig.  86)  the  varia- 

of  Mertmry,  tlie  great- 

lan  six  times  the  luaHt 

variaticng  of  apparent 

le  same  proportion. 

int  angular  magnitnde 

lole  diflkg  to  be  visible, 

their  own  ligbt.     Bat 

reflected  light  of  the 

can  be  seen  which  are 

nn  and  from  the  earth. 

ow  that  the  pn^portion 

tantly  diminisheB  as  the 

Kdnhuger. 


ov  vnK  ov  fCMtife. 

distance,  or  in  snperior 
illuminated  hemisphere 
t  moves  areund  and  ap- 
heauspheie  is  gradually 
greatest  dongation,  M 
▼istblA,  and  tibe  phuMt 
PC  seoMid  qnaitsr.  As 
the  sppMvnt  visible  dUc 
whioh  beeomes  iSbSwatst 
lestliesaiL 

I  of  Jf«Mwy  at  yaifaMH 
n.  The  plpiife  will  ap- 
«  the 


This  occurs  about  half  way  between  greatest  elongation 
and  inferior  conjunction. 

In  consequence  of  the  changes  in  the  brilliancy  of  these 
planets  produced  by  the  variations  of  distance,  aud  those 
produced  by  the  variations  in  the  proportion  ot  illuminated 
disk  visible  ^m  the  earth,  partiaHyTSmnpensating  each 
other,  their  actual  brilliancy  is  not  subject  to  such  great 
variations  as  might  have  been  expected.  As  a  general  rule, 
J<«fOTffy  shines  with  a  light  exceeding  that  of  a  star  of 
the  first  magnitude.  But  owing  to  its  proximity  to  the 
sun,  it  can  never  be  seen  by  the  naked  eye  except  in  the 
west  a  short  time  after  sunset,  and  in  the  east  a  little  be- 
fore sunrise.    It  is  then  of  necessity  near  the  horicon,  snd 


tiwreiore  does  not  seem  so  bri^tas  if  it  were  at  a  graafeer 
aUitade.  In  our  Jatitndeiwe  mig^t  almost  say  that  it  is 
never  visible  exoapt  in  the  morning  or  evening  twiUdit 
In  hif^  latitndsa,  or  in  ngions  whnw  the  air  is  Ms 
tnMpaiBBt,  it  ia  soaroefy  ever  visible  without  &  teksoope. 
It  is  nii  tiwt  OonunoDa  died  without  ever  obtaining  a 
viaw  ef  lilt  flMMi  JTsrvury. 

On  the  olhar  hand,  the  planet  Fsihm  ii;  next  to  the  sun 
and  moon,  the  moat  biiliant  object  in  the  heavans.  It  is 
so  mnqii  brlf^iter  than  any  fixed  star  fluit  there  oan  seldom 
he  aaj  dJibaUy  in  iden^jping  it.  The  unpraetiaed  ob- 
server ib||^  vndar  sene  drenfiBtanoas  find  a  diflleulty  in 


jtmsMA 


il^ 


814 


ABTBONOMT. 


distinfniiBhing  between  Venug  and  Jupiter ^  bnt  the  differ- 
ent motions  of  the  two  planets  will  enable  him  to  distil^ 
gnish  them  if  they  are  watched  from  night  to  night  dur- 
ing several  weeks.  .  . 

g  a.    ABFBOT  AHD  ROTATION  OV  MXBOUBT. 

The  varions  phases  of  Mercury t  as  dependent  npon  it3 
yarions  positions  relative  to  the  snn,  have  already  been 
diown.  If  the  planet  were  an  opaque  sphere,  without  in* 
equalities  and  without  an  atmosiriiere,  the  apparent  disk 
would  always  be  bounded  by  a  oinsle  on  one  side  and  an 
ellipse  on  the  other,  as  r^resented  in  the  flgnre. 
Whether  any  variation  from  this  simple  and  perfect  form 
basjivier  bemi  detected  is  an  open  qn^MtkMi^  the  balanee  of 
evidenoe  being  very  sfanmgly  in  the  negiliTa  Sfaioe  no 
spots  are  vidble  upon  it,  it  would  follow  ihat  unksi  vari- 
atioui  of  form  due  to  InequaUtieB  on  its  surfiuse,  sneh  as 
mountains,  can  be  deteeled,  it  is  impossible  to  (btermine 
wh^fiT  tile  planet  rotatee  on  its  axis.  The  only  evidence 
in  lavwr  of  nch  vetatioii  iathat  of  SoHsSras,  the  eaMbsftted 
astretuHner  of  IflienUul,  wlw  made  the  telflM(^  study 
of  tito  moon  and  planets  his  pindpal  woric.  About  the 
beginning  of  the  present  century  he  noticed  that  at  certain 
tiineB  the  south  horn  of  Hie  cresoent  of  Jf«»vMry  seemed 
to  be  blunted.  Attributiiig  tins  appetnuMb  io  \kk  duidow 
of  a  lofty  mountain,  he  eooiduded  tluiitiiib  l^^aiiM,  JfifiVMry 
revolved  on  its  axis  in  a  little  more  tlttn  %^i  ImMos.  But 
this  planet  has  sinee  been  studied  with  inr^ownMis  weaA 
more  powerful  than  those  of  SoaaSmnt,  fMSt 
Hoa  of  Us  rsMilts  has  been  obtidiM.  We  ni||i 
eottolude  that  the  pwiod  of  volition  of  Mt0trM  on  ill 
axis  fa  entirely  nntorown. 

an  atnuMpbere  of  JfMVNvy,  tiw  fjNKtoflt  ii 


!l 


sfMctram  «f  iUk 


'-•"•^'^j^' 


VaS^^^^nsi^i^Maitekv ' 


ifbiyindtthnkil^ 


"•- ^Y""'-^--'T\WtgUi 


r. 

Jupiter,  but  the  diifer- 
rill  enable  him  todistiikk 
pom  night  to  night  dnr- 


[ON  OV  MBBOUBT. 

f,  as  dependent  npon  ita 

gun,  have  already  been 

Mqne  sphere,  without  in- 

(here,  the  apparent  disk 

irele  on  one  i^de  and  an 

resented  in   the  figure. 

ample  and  perfect  form 

I  qniitioi^  the  btlanoe  of 

the  negitiTe.    ffinoe  no 

1  follow  that  unlesi  Tari- 

I  on  its  sorfaee,  soeh  as 

impossible  to  dMermine 

axis.    The  only  evidence 

f  SoHB&m,  the  oeWntted 

tad*  the  tdesoopie  skndy 

Indpalwork.    About  ihe 

f  henotioed  that  at  certain 

■cent  of  Jf«ro«ry  seemed 

I  appewMMb  ^  ^  AtOom 

id  ihtitivb  -^H^  Mttomty 

Bor^thm  »!  iMMurs.    Bat 

jdwfth  inrxrnnMBls  noiBh 

tfiMi.    We^nMipiMfom 
Aition  of  JfMNtoyoB  its 

f  jrM«wy,l3wt$fitefliis 
gildtthaliliyfii^^ 


ASPROTS  OF  MBROUnY 


810 


coincide  with  those  of  the  snn.  Of  course  we  should 
•expect  this  because  the  planet  shines  by  reflected  solar 
li^t  But  he  also  finds  tiiat  certain  lines  are  seen  in  the 
spectrum  of  Merewry  which  we  know  to  be  due  to  the  ab- 
sorption of  the  earth's  atmosphere,  and  which  appear 
more  dense  than  they  should  from  the  simple  passage 
throu^  our  atmosphere.  This  would  seem  to  show  that 
Merewry  has  an  envelope  of  gaseous  matter  somewhat  like 
our  own.  On  the  other  hand,  Dr.  Zollmeb,  of  Leipsic, 
by  measuring  the  amount  of  light  reflected  by  the  planet 
at  various  times,  concludes  that  Merewry,  like  our  moon, 
is  devoid  of  any  atmosphere  sufficient  to  reflect  the  lig^t 
of  the  sun.  We  may  therefore  regard  it  as  doubtful 
whether  any  evidence  of  an  atmosphere  of  Mereury  can 
be  obtained,  and  it  is  certain  that  we  know  nothing  defi- 
nite respecting  its  pl\yuoal  oonstitation. 


AVD  BUFPOaBD  BCTATIOK  OW 

vnruB. 


As  Fmmm  sometimes  comes  neater  the  earth  than  any 
other  primary  planet,  astKmomera  have  examined  its  snr- 
faoa  uriHk  graal  interest  ever  since  ^  inventi(m  ci  the 
tdeseope.  But  no  oonehiaive  evidence  respecting  the  ro- 
tation of  tiie  phaet  and  no  proof  of  any  ehaages  or  any 
inequalities  en  its  suRboe  hav«  ever  been  obtafaied.  The 
dMrvatioiit  am  either  Tery  diseordMit,  or  so  diiBeatt 
and  vDNttible  diet  w<e  mi^  readtty  nq^pose  the  ob- 
serv«n  to  btve  Inmb misled  as  to whattlwy  saw.  In  1767 
OissdA  tiroimiM  bft  saw  «  bright  spot  on  Vmm  te^ng 
aevsMl  mwfisirifii'  •vndiiyiy  nd  eon^adsd,  fram  Us  msp^ 
yomAJtkmmnaku<Smik»iit^^  onitsadtii  • 

UttbmtitethaiPkttlMmn.    The  snlqeatwM  next  tdM 
by  BLUWiii^  u  ItaMw  astroMnMr,  irbo.mppmi 
he  flitw  *  SMite  <iif  4mIe  f«|^OM  OB  <i^ 
eiwildbMd  to  bt  iMS  or  oeeaas,  tad  his  if0t  m  ftr  it  t6 
giv^  diMt  niaisA^    WatdiiBg  tham  fkom  Bi|^  to  night, 


816 


ABTBONOMY. 


he.oondnded  that  the  time  of  rotation  of  Ventu  was  more 
than  24  days.  Again,  Sohbotes  thought  that,  when  Ve^ 
nus  was  a  crescent,  one  of  its  sharp  points  was  blunted 
at  certain  intervals,  as  in  the  case  of  Mercury.  He  formed 
the  same  theory  of  the  cause  of  this  appearance— namely, 
that  it  was  due  to  the  shadow  of  a  high  mountain.  He  con- 
cluded that  the  time  of  rotation  found  by  Gassiki  was  near- 
ly correct.  Finally,  in  184S,  Db  Yioo,  of  Kome,  thought 
he  could  see  the  same  dark  regions  or  oceans  on  the  planet 
whidi  had  been  seen  by  Blanohini.  He  concluded  that  the 
true  time  of  rotation  was  23''  21"  22*.  This  result  has  gone 
into  many  of  our  text-books  as  conclusive,  but  it  is  contra- 
dicted by  the  investigation  of  many  excellent  observers 
with  much  better  instmments.  Hkbsohbl  was  never  able  to 
see  any  permanent  markings  on  Venus.  If  he  ever  caught 
a  glimpse  of  spots,  they  were  so  transient  that  he  could 
gather  no  evidence  respecting  the  rotation  of  the  planet. 
He  therefore  concluded  that  if  they  really  existed,  they 
were  due  entirely  to  clouds  floating  in  an  atmosphere,  and 
that  no  time  of  rotation  could  be  deduced  by  observing 
them.  ItuB  view  of  Hebsohbi.,  so  far  as  concerns  the 
aspect  of  the  planet,  is  confirmed  by  a  study  with  the  most 
powerful  telescopes  in  recent  times.  With  the  great 
Washington  telescope,  no  permanent  dark  spots  and  no 
regular  hhmting  of  either  hom  has  ever  been  observed. 

It  may  seem  curious  that  skiUed  observers  oould  have 
been  deceived  u  to  what  they  saw ;  but  we  must  remem- 
ber that  there  are  many  celestial  phenomma  which  are  ex- 
trem^jr  diffienlt  to  miike  ovt  By  looking  at  a  drawing 
of  a  planet  or  nebula,  and  seeing  how  pli^  every  thing 
seams  in  the  {rieture,  wemay  be  oi^ly  deceived  as  to  the 
aotnal  aspect  with  a  telesoope.  Under  tftedremnstaneqi,  if 
the  observer  has  any  preeonoeived  thfeory,  it  is  veiy  eaqr 
fcnr  him  to  think  he  aeei  eveiy  tbing  in  aeoortoMe  urith 
thattiieory.  Kow,  thaie  are  at  all  times  gnsttdiileraneei 
in  ihe  brimaaAy  of  thediiierMit  pMrtsol^  disk  of  F«m«ic 
It  is  brightest  near  the  rooild  e(|ge  wMch   'm  tUMd 


<m^fsssmiBmmtmam!miiiia 


ion  of  Vmiu  was  more 
bought  that,  when  F«-. 
\rp  points  was  blunted 

Mercury.  He  formed 
8  appearance— namely, 
igh  mountain.  He  con- 
id  by  Gassini  was  near- 
ly loo,  of  Rome,  thouj^t 
I  or  oceans  on  the  planet 

He  concluded  that  the 
2*.   This  result  has  gone 
elusive,  but  it  isoontra- 
uiy  excellent  observers 
BsoHVL  was  never  able  to 
nus.    If  he  ever  caught 
transient  that  he  could 
rotation  of  the  planet, 
they  really  existed,  they 
ig  in  an  atmosphere,  and 
)  deduced  by  observing 
,  BO  far  as  oonoems  the 
[)y  a  study  with  the  most 
imes.     With  the  great 
nent  dark  spots  sad  no 
IS  ever  been  observed, 
id  observers  oonid  have 
w  ;  but  we  must  remem- 
jhenonien*  which  are  ex- 
By  looking  at  a  drawing 
g  how  ph^  every  thing 
niirely  deoaived  as  to  the 
ndertheciroiiiiMtaiMKs,  if 
id  thisoiy,  it  is  Tsiry  eaqr 
Mag  in  aeeontaMe  wiHi 
iB  times  giiMit  difleranoet 
tttsoitlitf  diiko#  Vmm. 

vigB  wUdb  is  tttiBid 


MiBilii 


MiaBiiMi 


ABPB0T8  OF  VENUS. 


A 

817* 


toward  the  sun.  Over  a  small  space  the  brightness  is  such 
that  some  recent  observers  have  formed  a  theory  that  the 
sun's  light  is  reflected  as  frmn  a  mirror.  On  the  other 
hand,  near  the  boundary  between  light  and  darkness,  the 
surface  is  much  darker.  Moreover,  owing  to  the  undu- 
lations of  our  atmosphere,  the  aspect  of  any  planet  so  small 
and  bright  as  Vemu  is  constantly  changing.  The  only 
way  to  reach  any  certain  conclusion  respecting  its  ap- 
pearance is  to  take  an  average,  as  it  were,  of  the  appear- 
ances as  modified  by  the  undulations.  In  taking  this  aver- 
age, it  is  very  easy  to  inugine  variations  of  light  and  dark- 
ness which  have  norealexisttnce ;  it  is  not,  therefore,  sur- 
prising that  one  astronomer  should  follow  in  the  footsteps 
of  another  in  seeing  imaginary  markings. 

▲tmoaphere  of  Venus. — Xt^e  evidence  of  an  atmosphere 
of  Vmut  is  perhaps  more  conclusive  than  in  the  case  of 
any  other  planet.  When  Vmru  is  observed  voy  near 
its  inferior  conjunction,  and  when  it  therefore  presents  the 
view  of  a  very  thin  .crescent,  it  is  found  that  this  orescent 
extends  over  more  than  180°.  This  would  be  evidently 
impossible  unless  the  sun  illuminated  more  than  one  haU 
the  pbaafe  One  of  the  most  fortunate  observers  of  this 
phenomenon  was  Professor  G.  S.  Lr..^AN,  of  Yale  GoUege, 
who  observed  Vmut  in  December,  1866.  The  inferior 
oonjunotiom  of  the  planet  occurred  near  the  ascending 
no^,  so  that  its  angdar  distaaoe  from  the  sun  was  lass 
than  it  had  been  at  any  former  time  during  the  present  een- 
tury.  Professor  Lrwa  saw  the  disk,  not  as  a  thin  ores- 
omt,  but  as  an  entire  and  extremely  fine  oirde  ci  li|^t. 
Wis  therb-ore  condude  that  V(miu  hss  an  atmosfiliere 
whioh  ezeroisfls  so  powerful  a  refraotifm  upon  the  H^t  of 
the  son  that  the  latter  illuminates  several  degrees  more 
than  one  half  the  |^obe.  A  phmomeiion  whidk  must  be 
attribated  to  the  same  cause  hss  sevend  times  been  ob- 
sapv«ddu&ig  tkanaits  of  VeMU.  Ihiiti^  the  traarit  of 
IkiftmAm  d&,  1874,  most  of  tibe  obaerven  who  enjoyed 
a  fine  Hcm^  atmoi^ere  saw  that  when  Fmmw  was  par- 


MMM 


818 


A8TB0N0MT. 


tially  projeofeed  on  the  mm,  the  outline  of  that  purt  of  iti 
disk  oatside  tho  sun  ooold  be  dittingoiahed  by  a  delicate 
line  of  light.  A  similar  appearance -WMnotieadbjDaTiD 
RriTBffHousK,  of  Philadelphia,  on  June  8d,  1769.  From 
these  several  observations,  it  would  seem  that  the  refractive 
power  of  the  atmosphere  of  Vmu9  is  greater  than  that  of 
the  earth.  Attempts  have  been  made  to  determine  its  ex- 
act amount)  but  they  are  too  uncertain  to  be  worthy  of 
quotation. 


ft  4.  T&Airarra  ot  kbboubt  akd  ynrns. 

When  Mermvry  or  F^niM  passes  between  the  earth  and 
sun,  so  as  to  appear  projected  on  the  sun's  disk,  the  phe- 
nomenon is  called  a  tramii.  If  these  planets  moved  around 
the  sun  in  the  plane  of  the  ecliptic,  it  is  evident  that 
there  would  be  a  transit  at  every  inferior  conjunction.  But 
since  their  orbits  are  in  reality  inclined  to  the  ecliptic, 
transits  can  occur  only  when  the  inferior  conjunction  takes 
place  near  the  node.  In  order  that  there  may  be  a  transit, 
the  latitude  of  the  planet,  as  seen  from  the  earth,  must 
be  less  than  the  angular  semi-diameter  of  the  sun — ^that  is, 
less  than  16'.* 

The  lon^tnde  of  the  descending  node  of  Merewry  at  the 
present  tune  is  337",  and  therefore  that  of  the  ascending 
node  47°.  The  earth  has  these  longitudes  on  May  7th  and 
November  9th.  Since  a  transit  can  occur  only  within  a 
few  degrees  of  a  node,  Mwcwry  can  transit  only  within  a 
few  days  of  these  epoehs. 

The  longitude  of  the  descending  node  d  Fmmm  is  now 

•  Tlie  nstbciiMUori  stiidsnt.  loMmiiutttMtttM  laoliBatkmof  thsoi^ 
or  Jr«r«Nfy  hr  y  sad  thrt  of  y«M»Vt^\  wfll  faA H saiulMSsMH 
prabtaa  tooslenlste  On  HmiisoCdMaaoeflnaittMMdsWilUiiwkidii  la- 
ieiior  oonjonotkn  most  tsks^aos  teoiderttsta  tnasttnurc 


K    I 


'vm'^m'mmir ■ 


TRANSITS  OF  MERCVRT. 


nt 


ine  of  that  part  of  iti 
igniihed  by  a  delicate 
imMiMtteed  bj  Datid 
Tune  8d,  1769.  From 
eem  that  the  refractive 
is  greater  than  that  of 
deto  determine  its  ex- 
irtain  to  be  worthy  of 


IT  AMD  vMinni. 

between  the  earth  and 
le  sun's  disk,  the  phe- 
B  planets  moved  aronnd 
»tio,  it  is  evident  that 
erior  conjunction.  But 
islined  to  the  ecliptic, 
erior  conjunction  takes 
there  may  be  a  transit, 

from  the  earth,  must 
ter  of  the  sun — ^that  is, 

node  of  Mercury  at  the 
that  of  the  ascending 
gitudes  on  May  7th  and 
n  occur  only  within  a 
n  tramit  only  within  a 

;  node  of  Vemu  is  now 

•t  tbe  iaoUaatkNi  of  the  acUt 
r.wmfladHanJBiwailii 
MBtttaods^lttlBwhkhla- 
er  tlMt «  tiwHit  aaj  eeenr. 
■trie  iMltada  aM^  M  flnmd 


aUMsgiMlar  ft 
■■iBDBiMlna.  uA 


about  S56°,  and  therefore  that  of  the  ascending  node  is 
76**.  The  earth  has  these  longitudes  on  June  6th  and  De* 
oember  7th  of  each  year.  Transits  of  Venut  can  there« 
fore  occur  only  within  two  or  three  days  of  these  tiroes. 

Beounenoe  of  Transits  of  Meroury.— The  tnuieite  of  Mer- 
eurp  and   Vmui  recur  in  eyelet  which  reaemble  the  eighteen- 

irear  cycle  of  eclipies,  but  in  which  the  precision  of  the  recurrence 
■  leae  eMking.  From  the  mean  motions  of  Meremry  and  the  earth 
already  given,  we  Und  that  the  mean  eynodic  period  of  Mereury  ia, 
in  dedmala  of  a  Julian  year,  Oi'-  8179M.  Three  aynodic  period*  are 
therefore  aome  e^teen  daya  leas  than  a  year.  I^  then,  we  suppose 
an  inferior  cmninnotioa  of  Meratrf  to  occur  exactly  at  a  node,  the 
third  conjunction  foUowing  will  take  phww  about  eighteen  daya 
before  the  earth  again  reachea  the  node,  and  therefore  about  18" 
from  the  node,  since  the  earth  moves  nearly  1*  in  a  day.  This  is 
far  outside  the  limit  of  a  transit ;  we  mu^  therefore,  wait  until 
another  conjunction  occurs  near  the  same  place.  To  find  when 
thia  will  be.  the  successive  vulgar  fractions  which  converge  toward 
the  value  of  the  above  period  may  be  found  by  the  method  of  oon- 
tinued  fractions.    The  first  five  of  these  fractions  are  : 

i      A      »'f      H      ^ 

Here  the  denomiaaton  are  numbers  of  synodic  periods,  while  the 
numeratorB  are  the  approxtanate  corresponding  number  of  years. 
By  actual  multiplication  we  find  : 


8 Periods:.-  Or  MITW  =    1' - 

19      «        =  «087864=>     •  + 

n    "     =  9vt9m=   7- 

41    "     =  is-<Nrr«6=  18  + 

145     •'       =  46001180=  48  + 


04a»». 

087864. 


068110. 


Error  =  -  17' 

•     =  +  10* 

••  —   7* 

••    =  +  r-i 
»   «+  tr-n 


In  tUs  table  the  erron  show  «he  waaOitft  of  AagMss  fmi  Aw 
node  at  whick  the  inferior  coaJnnetioB  will  oeenr  at  t)M0M  of  «ai 
year,  rix  yevra,  srrea  yemrs,  etc.  Tlisf  are  fiiHid  bj  swUtii^yiai 
UiefiBstimibywhiflhtiMlatervabeaesMl  or  Ml  i^vt  of  •■  MtM 
nnariMro(yMntb7  880*.  ItwUlbesenthat  tke  18th,sa4,^ii 
and  146th  oonJuaMoaa  oooar-nemer  sad  neawr  ttw  aOM,  sr,  s«|^ 
posiag  thai  we  do  not  start  from  a  mtda,  asam  aM  MMW  Ito  |iii||. 
of  the  ofMta  fima  which  we  do  start  It  foilims  that  tba  vpsa^ 
lof  atraasltof  Jfovuryat  the  sbms  ao4a  is  poaailils  al  UK 


end  of  7  fsan,  prabaUa  at  the  end  of  18  years,  and  alaMSt  esttain 
at  ti»oiMl^  40  yean.    Hm  lattor  is  the  ^le  wbieh  it  wwidd  be 


tabseaigr 


to  take  as  that  im  mhSch  aU  the  traaslts  would 
.  but  it  wwdd  stlHaotbeso  exaet -as  the  eellpss  cjck  of  18 
ysais  11  &^. 


8«0 


AaTBONOMY. 


Tin  following  table  ihowi  the  datee  of  ocouimmoe  of  tnuuito  ol 
Jftrawy  durins  the  preeent  centurj.  They  are  Mpuated  into  Mny 
tnuultL  whioh  ooonr  nenr  the  deecending  node,  md  NoTember 
ones,  wnidi  oocur  near  the  aeoending  node.  November  trandto  an 
the  most  muneroua,  beoauae  JKfreioy  is  then  nearer  the  sun,  and 
the  transit  limita  are  wider. 


3S 

/  » 
Z  5 


Vm,  May  6. 
1889,  May  8. 
1848,  May  8. 
1878.  May  «. 
1881.  May  9. 


/5 

7 
'  J 

(i 

7 
/  3 

I  $ 

I  3 


1808.  Not.  8, 
1818.  Not.  11, 
18M.  Not.  S. 
188S.  Not. 
1848,  Not 
1861,  Not. 
1888.  Not. 
1881,  Not, 


7. 
10. 
19. 

8. 

7. 


1804.  Not.  10. 


/f/^ 


It  will  be  seen  tliat  in  a  cycle  of  48  years  thei^  are  two  May  tran- 
sits and  four  NoTember  ones,  so  that  the  latter  are  twioe  as  nu- 
maroos  as  the  former.  These  numbers  may,  IwweTer,  change  slightly 
at  some  future  time  through  the  failure  of  a  recurrence,  «r  the  en- 
trance of  a  new  tran^  into  the  series.  Thus,  in  the  May  series,  it 
is  doubtful  whether  there  will  be  an  actual  truisit  46  years  after 
1801— that  is,  in  1987— or  whether  JTsrmfy  will  only  nass  Tory  near 
the  limb  of  this  sun.  On  the  other  hand.  JftrBwry  passea  within  a  few 
minutes  of  the  sun's  limb  on  May  8d,  1868,  and  it  will  mobably 
graio  the  Hmb  46  years  bter— that  is,  on  May  4th  or  8th,  1911. 

BMrnrrniM  or  Tnmita  of  voniM.— For  many  centuries 
past  and  to  come,  tranrits  of  FShmm  oocur  in  a  cycle  more  exact  than 
Oiose  of  JfsrvNnr.  It  hi^pens  that  dght  ttanes  the  mean  .  Mttion  of 
I^Mtt  ia  Tory  nearly  the  same  aa  thirteen  times  the  meaii  motion 

of  the  earth;  in  other  words,  Vrnvu 
makes  18  rerolutions  around  the 
son  in  nearly  the  same  time  that 
the  earth  makes  8  rsrolutlons— 
that  ia,  in  eight  yean.  During 
this  period  than  wUl  be  6  inferior 
eoaijiinetionaof  Vmut,  becanae  tiie 
lallar  hM  made  6  randutioaa  mon 
ttan  the  eaith.  OMMeq(aen*ly,  if 
we  wait  eigiit  yean  ftom  an  inferior 
floqjuaetion  of  Fsmh^  we  shalL  at 
the  end  o|  that  tlme^  hwre  aaouer 
inferior  ecajonotioB,  ihi  flfth  in 
Mndar  order,  at  nearly  the  same 
mttat  of  the  two  ocMta.  It  wfll, 
flMnfon,  oeoir  1^  the  I 
of  the  year,  and  in  aan^  the  I 
position  MlatiTe  to  the  node  of  FsMM.  bVlg.  SSletdi 
Um  mn,  and  the  dnde  drawn  around  It  the  orbit  of  ^  earth. 


BlilBjM^aM^llli!^i«B^y»t.^ 


f  occuirnmoe  of  tnuuiu  ot 
1*7  an  Mparsted  into  May 
ing  node,  and  Novwiber 
le.  November  truuita  m 
then  nearer  the  tun,  nnd 


TRANBira  or  vknub. 


331 


18M,  Not.  «. 
181S.  Nor.  11. 
1899.  Not.  5. 

1880.  Not.  7. 
1848.  Not.  10. 
1801.  Not.  19. 
1808.  Not.  8. 

1881.  Not.  7. 

[   1804.  Not.  10.   ><-/(/ 

irs  ttwre  are  two  May  tran- 
Im  lataterare  twloe  aa  nu- 
jr,  howerer,  change  alightly 
of  a  lecarrence,  «r  the  en- 
rhua,  in  the  May  wriea.  it 
Btnal  tnuuit  40  year*  after 
ny  will  only  paai  Tery  near 
Ifiireiwy  paiaea  within  a  few 
1805,  and  it  will  probd>ly 
May  4th  or  Stii,  Itll. 
ilM.— For  many  eenturiea 
in  a  cycle  more  exact  than 
i  timea  the  mean  '.  Mt^n  of 
m  timea  the  meau  motion 
arth ;  in  other  worda,  Vmm 
18  rerolntiona  anxiiid  the 
Marly  the  aame  time  that 
th  makea  8  reTohitlona— 
in  eight  yeara.  Doting 
iod  then  wUl  be  5  inferior 
itionaof  FbMM,  becanaethe 
B«  made  6  rartdutioaa  more 
•  emtt.  Oooaeq^wntly,  if 
d^  veam  f  mm  an  innnor 
ition  of  Fmim^  we  dmll,  at 
ol  that  timn^  hnve  aqoUMMr 
eoBJmietfoB,  iho  Uih  in 
order,  nt  nearly  the  aame 
f  the  two  MfUta.  It  wfU, 
occur  ak  the 


fa,  occur 

reM>,andinnenita[tha 
ta  fig.  8Slefc0ian«aant 
H  the  orbit  of  «be  ear^ 


*i;S'M:<*:.^»S'?m^*l!.:mi 


8unpoae  alio  that  at  the  moment  of  the  inferior  conjnnction  of 
Kmim,  we  draw  a  itndght  line  8 1  through  Vmvt  to  the  earth  at  1. 
We  ahall  then  haTC  to  wait  about  If  yeati  for  another  inferior  con- 
junction, daring  which  time  the  earth  will  haTc  made  one  ictoIu- 
tion  and  |  of  another,  and  Vmtu  9|  reTolution*.  The  straiBht  line 
drawn  through  the  point  of  inferior  conjtuiction  will  then  M  8  9. 
llie  third  conjunction  will  in  the  mme  way  take  place  in  the  poai- 
tion  S  8,  which  ia  1|  rcTolutiona  further  adTanoed ;  the  fourtn  in 
the  poaition  8  4,  and  the  ilfth  in  the  poaition  8  8.  If  the  corre- 
spondence of  the  motions  wen  exact,  the  sixth  conjnnction,  at  the 
end  of  8  yeara  (0  x  14  =  8),  would  again  take  phwe  in  the  original 
poaition  8 1,  and  all  subaequent  onea  would  follow  in  the  same 
order.  All  inferior  conjunctions  would  then  take  phuw  at  one  of 
these  Atc  points,  and  no  transit  would  CTcr  be  possible  unless  one 
of  thtae  pcnnts  should  chance  to  be  Tcry  near  the  line  of  nodes. 

In  fact,  howcTcr,  the  correapondence  is  not  perfectly  exact,  bat, 
at  the  end  of  8  years,  the  sixth  conjunction  will  take  place  not 
exactly  along. the  line  fi'l,  bnt  a  little  beforathe  two  bodiea  reach 
this  luie.  The  actual  angle  between  the  line  ^1  and  that  of  the 
sixth  conjunction  will  be  about  9°  99',  the  point  ahifting  back  to- 
ward the  direction  04.  Of  course,  each  followins  conjunction  will 
take  ;|^aoe  at  the  same  distance  back  from  that  of  mght  yean  befora, 
leaTing  out  amall  chugea  due  to  the  eccenuicitiea  of  the  OtMta  and 
the  Tariatimia  of  their  elements.  It  follows  then  that  if  we  rappMe 
the  fire  lines  of  conjunction  to  bare  a  retrograde  motion  m  a 
direction  the  op«oaite.of  that  of  the  arrow,  amoonting  to  9"  M'  in 
right  yeara,  all  the  inferior  conjunctions  will  take  jriace  along  theaa 
Htc  llnea.  The  distance  apart  of  the  linea  betag  79"  and  the 
motion  about  18'  per  year,  the  interTals  between  tiie  paaaagea  of 
the  aaTcral  conjonetion  lines  oTer  the  line  of  nodes  will  be  aboat 
940  yenra.    Really,  the  exact  time  is  948  years. 

Boppose,  now,  that  a  conjunction  should  take  phM»  exactly  at  a 
node,  then  the  fiftii  following  conjunction  would  take  ]^o 
9*  M'  befon  reachfcng  the  node.  The  Umitn  within  whidk  » tnHtit 
can  oeoor  an,  however,  only  1°  40'  on  each  side  of  the  Mdarnmi- 
seqiwnthr,  tharw  would  be  no  further  transit  at  that  node  mttl  the 
next  following  conjonetion  point  naehed  It,  wbkii  woaMh^ppMat 
the  end  of  MSyeata.  If,  howerer,  the  ooitiwietini  shooldtakejpbce 
between  0"  SO^and  1*  40'  tifUr  reaehli«  ^  nod%  then  wonUT be  a 
tnuiait,  and  the  Ulth  foOowing  conjoaottoii  wooM  also  ooaor  williin 
the  Umit  on  the  othw  aide  of  the  node,  so  thiat  we  ahoald  ham  two 
tranaita  eight  yean  apart  We  may,  thereon,  Iwre  ailher  one 
traadt  or  two  aeooid^  to  the  distance  from  the  node  at  iHdflii  the 
flnt  tnurit  ocean,  m  thna  haTc  at  a|iy  om  node  eiOiern  iliiie 
tranalt,  or  ajplr  of  trantita  dsht  yem  uMtr^B  •  <7d«  ol  »M  y«n. 
At  the  addme  of  thia  cycle  the  node  will  be  half  wi^  batwera  two 
of  tin  coajonetkm  pcinta— the  points  1  and  8,  for  inatance ;  bat  it  is 
eTUkmt  that  In  tUa  caae  the  qraoaite  node  wUl  eeindde  with  the 
con  jonotien  pdnt  9,  since  there  is  an  odd  nomber  of  aoeh  pointa. 
It  f<dto«a,  tifonfon,  that  dtoat  the  middle  of  tite  Interral  between 
two  cooaoentiTe  sets  <rf  tnAaits  at  one  node  we  shnU  hum  a  tnttrit 
orn  pafr  of  tntuita  at  thf8  (Opposite  node. 


332 


ABTRONOMT. 


Eilit 


Tho  earth  pmsm  through  th«  line  of  the  deeeending  node  of  the 
orbit  of  K«i«M  ewrlx  in  June  of  eeoh  yew,  ud  through  the  MModiuff 
node  enrly  in  December.  It  followe,  therefore,  that  the  leriee  will 
be  •  tmneit  or  a  pair  of  tnuuiti  in  June  ;  then  an  intenral  of  about  IM 
veart,  to  be  followed  by  a  transit  or  a  pair  of  transit*  in  December, 
and  so  on.  Owing  to  the  eccentricity  of  the  orbita,  the  interrals 
will  not  be  exactly  equal,  the  motiona  of  the  several  ooniunction 

Kints  not  being  uniform,  nor  their  diatanoe  exactly  79  .     The 
tee  and  interrala  of  the  traneite  for  three  cyoiea  nearest  to  the 
present  time  are  as  follows  : 

1S18,  June  %.  1701,  Jun«  S.  9004,  Jane  8. 


1898,  June  1. 
1681.  Deo.  7. 
1888.  Deo.  4. 


1708.  Jane  8. 
1874,  Deo.  9. 
1888,  D«c.  6. 


9019,  Jane  6. 
9117,  Dee.  11. 
9198,  Dm.  8. 


Intwvala. 
8  years. 

lOOi    " 

8      •• 

191*    " 


1*he  9487ear  cycle  i«  so  exact  that  the  actual  deviations  from  it 
nre  due  almoet  entirely  to  the  secuUr  variation  of  the  orbits  of 
Ymut  and  the  Earth,  Moreover,  the  conjunction  of  December  8th, 
1874,  took  place  1°  96'  past  the  ascending  node,  so  that  the  con- 
iunotion  of  1883  tekes  pUce  about  1*  4'  before  reaching  the  node. 
Owing  to  tho  near  approach  of  the  period  to  exactness,  several  pairs 
of  transits  near  this  node  have  taken  place  in  the  past,  at  equal  in- 
tervals of  948  years,  and  will  be  repeated  for  three  or  four  cycle*  in 
the  fntnre. 

Nearly  the  same  remark  applies  to  those  which  take  place  at  the 
descending  node,  where  pairs  of  transits  eight  vean  apart  will 
occur  for  about  three  cyoles  in  the  future.  Owb|L  however,  to 
seenlar  vaiiaiiuns  of  the  orbit,  the  oonjunction  pdnt  lorthe  second 
June  transit  of  each  pair  and  the  first  December  transit  will,  after 
perhapa  a  tboosand  years,  Uk»  pboe  so  far  from  the  nod*  that  tho 
pbiMl  will  not  quite  touch  the  sun,  and  then  during  a  period  tA 
many  oentuiiaa  there  will  only  be  one  teanait  at  each  node  in 
•very  948  yean,  instead  of  two,  aa  at  present 


«8. 

Some  astronomerff  are  of  opinion  that  there  is  a  small 
planet  or  a  group  of  planets  revolving  around  the  son 
inside  the  orbit  of  Merewry.  To  this  supposed  phmet  the 
name  Vuioan  has  been  givoi ;  but  astronomers  generally 
disoradit  the  existenoe  of  sneh  a  planet  of  ooarfderaUe 
si«e,  because  the  ovidenoe  in  its  Urm  is  not  Ngirded  as 
condniiTe.  . 


nn»-mm»mim«mKmi  "i^mmnHim'tmuiiiamsjimwi^SB 


deMending  nodo  of  ths 
id  through  UM  Moendiiiji 
ton,  th*t  the  mtIm  wlU 
u  Ml  intenml  of  About  IM 
of  tmuiii  in  December, 
the  orbits,  the  interrala 

the  MTenl  ooniunction 
Moe  exMstlj  79%  The 
Be  cydee  newreat  to  the 


Jane  8. 
Jane  6. 
Dee.  11. 
Dm.  8. 


IntwvaU. 
8  jenre. 

lOSi    " 

8      " 


kctunl  devlntioni  from  it 
wintion  of  the  orbits  of 
■notion  of  DecemlMr  8th, 
(  node,  M  tlMt  the  con- 
efore  reaching  the  node. 
toexnctncM,  Mrerkl  pnira 
I  in  the  past,  at  equal  in- 
brtliree  or  four  oyolea  in 

B  which  take  place  at  the 
•  eight  Tean  apart  will 
ire.  Omag.  however,  to 
bUou  point  for  the  Moond 
eember  traaait  will,  after 
t  froaa  the  node  that  the 
then  during  a  period  <rf 
\muAi  at  each  node  in 
anL 


JKUOm  VLMMWrn. 

ihftt  there  is  «  snudl 
Iving  aronnd  the  mm 
it  snpposed  phaiet  the 
utrdnomen  generally 
planet  of  ooBrfderaUe 
wis  not  ngirded  as 


THB  SUPPOSED  VULCAN. 


8M 


The  evidence  in  favor  of  the  existence  of  such  planets  may  tie 
divided  into  three  classes,  as  follows,  which  will  be  considered  in 
their  order : 

(I)  A  motion  of  the  perihelion  of  the  orbit  of  Mtreury,  supposed 
to  M  due  to  the  attraction  of  such  a  planet  or  group  of  planets. 

(3)  Transits  of  dark  bodies  across  the  disk  oT  the  sun  which  have 
been  supposed  to  be  seen  by  various  otieervers  during  the  past  cen- 
tury. 

(8)  The  observation  of  certain  unidentified  objects  by  Professor 
Watson  and  Mr.  Lbwis  Bwirr  during  the  total  eclipse  of  the  sun, 
July  »iKh,  1878. 

(1)  In  1808,  Lb  Ycrkur  made  a  careful  collection  of  all  the  obser- 
vations  on  the  transits  of  Mtnury  which  had  been  recorded  since  the 
invention  of  the  telescope.  The  result  of  that  Investigation  was 
that  the  observed  times  of  transit  could  not  lie  reconcilra  with  the 
calculated  motion  of  the  planet,  as  due  to  the  gravitation  of  the 
other  bodies  of  the  solar  system.  He  found,  however,  that  if,  in 
addition  to  the  changes  of  the  orbit  due  to  the  attraction  of  the 
other  planets,  he  supposed  a  motion  of  the  perihelion  amounting  to 
86"  in  a  century,  the  observations  could  all  be  satisfied,  wch 
a  motion  might  be  produced  by  the  attraction  of  an  unknown 
planet  inside  the  orbit  of  Mereury.  Since,  however,  a  single 
planet.  In  order  to  produce  this  effect,  would  have  to  be  of  oui.  Td- 
erable  slse,  and  since  no  such  object  had  ever  been  observed  during 
a  total  eclipse  of  the  sun,  he  concluded  that  there  was  probably  a 
group  of  planets  much,  too  small  to  be  separately  distinguished. 
So  far  as  the  discrepancy  between  theo:  y  and  obwrvatlon  is  con' 
cemed,  these  results  of  Le  Vkhribb's  have  been  conmletely  con- 
firmed bv  the  mathematical  researches  of  Mr.  O.  W.  Uax,  and  by 
observations  of  transits  since  La  Ybbbibb's  calcutetions  were  com- 
pleted. Indeed,  the  result  of  these  researches  and  observations  is 
that  the  motioivof  the  perihelion  is  even  greater  than  that  found 
by  Lb  Ybbbibb,  the  suiplus  motion  being  more  than  40"  in  a  cen- 
tury. There  is  no  known  way  of  aotiountins  for  this  moCioB  in 
aooordanoe  with  well-eatabliriied  lawa,  exsept  oy  supposing  nMtter 
of  soma  sort  to  be  revolving  around  the  sun  in  the  suppcSed  posi- 
tion. At  the  saoie  time  it  ia  always  poadble  that  the  effect  may 
be  praduoed  \ij  some  oaknown  causa.* 

(8)  Astronomical  reoords  oontain  upward  of  twenty  iBstaaeea 
in  whi«b  dark  bodiea  have  bean  supposed  to  be  seen  in  transit 
aorasa  tlie  disk  of  the  son.  If  we  suppose  these  obaervatimia  to  be 
all  psrfeethr  eoRWt,  theexistenoe  of  a  great  number  of  ooasidaabla 
j^aaets  wlwla  the  oibit  of  Jbrewy  wookl  be  placed  beyond  doubt. 
Bat  a  oitkal  aaaMs  allows  that  Uieaa  observations,  eonsidarad  aa  a 
olasa,  an  aot  an^kM  to  tha  sUgl^eat  credeaae.    In  the  irai  plaM» 

*  Ab  ebotrD-dyaaada  theory  of  attmetkm  has  beea  wltldn  die  past 
twMtar  jMM  sMwastsii  hgrarvanl  Genaavahyalois;*.  which  lavaivaB 
a  and  varlrimnaat  tha  osdkMKT  thaory  of  gravitatto 


tthaoidlBaiTthaoryotgiravitattoB.  Ithaabaea 
sbMra  ttit,l9M|ioaiR«  fUa  dw%  tnie,  tta  BMthm  df  te  paittidloB 
of  Jfiway  o0Uhb»  aooooiUsd  for  bf  tha  aMmotkai  of  tta  I 


t!WJW."''4w,'.'Jt!ipa!iwswwii 


824 


ASTSONOitr. 


•OATcely  any  of  them  were  made  by  experienced  obaerren  with 
powernil  iutnunenta.  It  ia  very  eaay  for  an  unpractiaed  obaenrer 
to  miatake  a  round  solar  spot  for  a  planet  in  transit.  It  ma]f  there- 
fore be  supposed  that  in  many  cases  the  observer  saw  notlung  but 
a  spot  on  the  sun.  In  fact,  the  very  last  instance  of  the  kind  on 
record  was  an  observation  by  Wbbbb  at  Peckeloh,  on  April  4th, 
1870.  He  published  an  account  of  his  observation,  which  he  sup- 
posed was  that  of  a  planet,  but  when  the  publication  reached  other 
observers,  who  had  Men  ezamininff  the  sun  at  the  same  time,  it 
was  shown  conclusively  that  what  he  saw  waa  nothing  more  than 
an  unusually  round  solar  spot.  Amia,  in  mos*i  of  the  cases  referred 
to,  the  object  seen  was  describra  as  of  such  magnitude  that  it 
could  not  ndl  to  have  been  noticed  during  total  edipaes  if  it  had 
any  real  existence.  It  is  also  to  be  noted  that  if  such  planets  ex- 
isted they  would  frequently  pass  over  the  disk  of  the  sun.  Dur- 
ing the  past  fifty  years  the  sun  has  been  observed  almost  eveiv 
day  with  the  grMtest  assiduity  by  eminent  observers,  armed  with 

ewerfnl  instruments,  who  have  made  the  atudy  of  the  sun*s  snr» 
w  and  spots  the  prlndnal  work  of  their  lives.  None  of  these 
observers  has  ever  recordea  the  tranait  of  an  unknown  planet  Thia 
evidence,  thouygh  negative  in  form,  ia,  under  the  dreumstances,  oon« 
elusive  asainst  the  existence  of  such  a  planet  of  such  magnUode 
aa  to  be  ^sible  in  trandt  with  ordinary  instruments. 

(S)  The  observations  of  Professor  Watbox  during  the  total 
eclipse  above  mentioned  seem  to  afford  the  strongest  evidence  yet 
obtained  in  favor  of  the  real  exirtenoe  of  the  planet.  His  mode  of 
proceeding  waa  briefly  this :  Sweepiiw  to  tne  west  of  tlM  sun 
dnrina  the  eclipse,  he  saw  two  objects  m  positions  where,  snmioa- 
ing  m«  pointing  of  his  telesoope  accurately  known,  no  fixed  star 
ensted.  lliere Is,  however,  a  piur  of  known  stars,  one  of  which  is 
about  a  degree  distant  from  one  of  the  unknown  objects,  and  the 
othor  aborn  the  sane  distance  and  direction  frmn  the  aecmid.  It 
is  considered  by  some  that  Profeaaor  Watboii's  supposed  phnets 
Biay  have  been  this  pair  of  stara.  Still,  if  Professor  Watsos's 
iriaiiets  were  capable  of  produdng  the  motion  of  the  perihelion  of 
JftrmHy  already  refened  to,  we  aitonid  nguA  their  existenoe  as 
plaoed  bmrond  reasonable  doubt  But  his  dbservfttMoa  and  tbt. 
theorettoai  results  of  Ln  Ybbbiu  do  not  in  any  manner  streafthaa 
each  other,  because,  if  we  suppose  the  obsoved  perturbations  in 
the  orbit  of  Jfiwwifv  to  be  due  to  planets  so  soiall  as  thoae  seen  by 
WATioir,  tiie  number  of  these  pmnets  must  be  many  thovnaadi. 
Now,  it  ia  verv  certain  that  there  an  not  tlMusaaaa  ef  iNaaeti 
than  Mister  tban  Ou  sixth  magnitude,  because  thcry^MoIa  ham 
been  seen  by  other  teleaoopea  engaaed  in  the  mbm  search.  The 
matSkx  we  suppose  the  individnal  ^mets,  the  aarsnomteovs  O^y 
must  be,  and.  finally,  if  we  consider  them  asjodividaally  invisibli^ 
thnrwiUprababiyMinBbeiedbytaisof thoaaanda.  Theamaller 
•ad  mm  onmenMa  Ihsy  are,  sapnosiag  thair  ooabinad  masi  the 
aam,  the^Mrtar  ttaavm  total  of  li^t  they  wookl  niaei  At  a 
(tetab  jap  tha  amount  of  UtM  would  baooaa  ao  eoMManMa 
that  tm^ite  trwUd  appear  m  >  otond-llka  mass.    Hev,tlWMia 


MtMMRWimii 


THE  SUPPOSED  VULCAN. 


826 


lerienced  obaerren  with 
an  unpnctised  obienrer 
in  tranait    It  may  thera- 
tbaerrer  aaw  nothing  but 
instance  of  the  kind  on 
Peckeloh,  on  April  4th, 
•enraticn,  which  he  tap- 
publication  reached  other 
sun  at  the  same  time,  it 
'  waa  nothing  more  than 
moel'i  of  the  caaea  refemd 
such  munitude  that  it 
ig  totJeclipaea  if  it  had 
that  if  tuch  planeta  ex- 
j  diak  of  the  aun.    Dnr- 
m  obeerred  almost  eveiy 
int  obserrers,  armed  with 
lie  study  of  the  sun's  sur- 
leir  lives.    None  of  these 
an  unknown  planet    Thia 
ier  the  dreumatances,  con- 
planet  of  such  magidtade 
istruments. 

Fatsoh  during  the  total 
the  strongest  eridenoe  yet 
the  planet.  His  mode  of 
to  ttw  west  of  the  sun 
i  porilions  where,  sumioa- 
ately  known,  no  fixed  star 
lown  atars,  one  of  which  is 
unknown  objects,  and  the 
don  from  n»  aeeond.  It 
^ATaoH's  supposed  planets 
U,  if  Professor  WAxaoa'a 
Hilion  of  the  perihelion  of 
nguA  tlMir  existence  aa 
hia  obaerraitHiiis  and  th^ 
t  in  any  manner  str«q[thMi 
observed  perturbations  in 
I  so  small  as  thoae  seen  by 
must  be  maoy  tbousanda. 
not  tiMosaada  of  phUMta 
',  beeaose  theywula  Vvn 
in  the  snm*  aearoh.  Ite 
te,  the  awra  mnnteoas  Oi^y 
m  asladiTidnaUy  iuTlstble. 
of  thouaaBda.  ThewMller 
gthdr  oooriiiiMdBMBtiM 
( they  would  niMt  At» 
lid  beeoM  so  eoMManMa 
i4Uw  aMB.    Nov,  flierels 


a  phenomenon  known  as  the  zodiacal  light,  which  is  probably  caused 
by  matter  either  in  a  gaseous  state  or  composed  of  small  particles  re- 
volving around  the  sun  at  various  distances  from  it.  This  light 
can  be  seen  riring  like  a  pillar  from  the  western  horizon  on  any 
very  clear  night  in  the  winter  or  spring.  Of  its  nature  scarcely 
any  th^  is  yet  known.  The  spectroscoi^c  observations  of  Pro- 
fessor T^iOBT,  of  Tale  GoUese,  seem  to  indicate  that  it  is  seen  by 
reflected  sunlight.  Very  different  views,  however,  have  obtained 
respecting  its  constitution,  and  even  its  position,  some  having  held 
that  it  is  a  ring  surrounding  the  earth.  We  can  therefore  merely 
sun^t  the  possibility  that  the  observed  motion  of  the  perihelion 
ofjurvury  is  produced  by  the  a('  -  .l. 


I  attractton  of  this  mass. 


I«BM5R»3 


JT^l'^liiSBIB 


CHAPTER  IV. 
THE  MOON. 

In  Chapter  VII.  of  the  preceding  part  we  have  de- 
scribed the  motions  of  the  moon  and  its  relation  to  the 
eartL  We  shall  now  explain  its  physical  constitution  as 
revealed  by  the  telescope. 

When  it  became  clearly  understood  that  the  earth  and 
moon  wei«  to  be  regarded  as  bodies  of  one  class,  and  that 
the  old  notion  of  an  impassable  gulf  between  the  character 
of  bodies  celestial  and  bodies  terrestrial  was  unfounded, 
the  question  whether  the  moon  was  like  the  earth  in  all  its 
details  became  one  of  great  interest.  The  oo., '  of  most 
especial  interest  was  whether  the  moon  cc  '  i  e  the 
earth,  be  peopled  by  intelligent  inhabitants.  *  ingly, 
when  the  telescope  was  invented  by  Gaulw),  one  of  the 
fint  objects  examined  was  the  moon.  With  every  im- 
provement ot  the  instrument,  the  examination  became 
more  thorough,  so  that  the  moon  has  been  an  object  of 
carafnl  study  by  the  phyrical  astronomer. 

The  immediate  Bucoe8M>n  of  Gauuo  thoni^t  thafc  they 
peieeived  the  snrfaoe  of  the  moon,  like  that  of  our  globe, 
to  be  divenified  with  hadand water.  Certain  regions  ap- 
peared dark  and,  for  the  most  part,  pmooth,  while  others 
wera  bright  and  evidently  broken  up  Into  hilband  vaDeys. 
The  former  regions  wefe  supposed  to  be  ooeHia,  and  w- 
odved  names  to  correspond  with  this  idea.  These  naoMa 
ormtlnue  to  the  present  day,  although  we  now  know  that 
there  are  no  ooeans  there. 

With  evoiy  improvwnent  in  the  meaaa  of  naatroiit » 


TH«  MOON. 


897 


v. 


ig  part  we  have  de- 
d  its  relation  to  the 
ysical  constitation  as 

)d  that  the  earth  and 
of  one  class,  and  that 
between  the  character 
[trial  was  unfounded, 
ike  the  earth  in  all  its 
The  t>Oi.  ^  of  nioet 
moon  cc  '  a-e  the 
ntantB.  .»n  Ingly, 
'  Galilbo,  one  of  the 
ion.  With  every  im- 
examination  became 
as  been  an  object  of 
omer. 

iLBO  thoui^t  that  they 
like  that  of  onr  globe, 
.  Certain  r^ons  ap- 
,  pmooth,  whUe  othws 
p  Into  hnbaad  vall^fa. 
to  be  006MU,  vaA  re- 
b  idea.  TheaeiiMiMa 
l^we  now  know  titii 

meana  of  iaMii«h,it 


has  become  more  and  more  evident  that  the  surface  of  the 
moon  is  totally  unlike  that  of  our  earth.  There  are  no 
oceans,  seas,  rivers,  air,  clouds,  or  vapor.  We  can  hardly 
suppose  that  animal  or  vegetable  life  exists  under  snc^ 
circumstances,  the  fundamental  conditions  of  such  ex- 
istence on  our  earth  being  entirely  wanting.  We  might 
almost  as  well  suppose  a  piece  of  granite  or  lava  to  be  the 
abode  of  life  as  the  surface  of  the  moon  to  be  such. 

Before  proceeding  with  a  description  of  the  lunar  sur- 
face, as  made  known  to  us  by  the  telescopes  of  the  present 
time,  it  will  be  well  to  give  some  estimates  of  the  via- 
bility of  objects  on  the  moon  by  means  of  our  instruments. 
Speaking  in  a  rough  way,  we  may  say  that  the  length  of 
one  mile  on  the  moon  would,  as  seen  from  the  earth,  sub- 
tend  an  angle  of  1'  of  arc.  More  exactly,  the  angle  sub- 
tended would  range  between  O'-S  and  0'-9,  according  to 
the  varying  distance  of  the  moon.  In  order  that  au'ob- 
ject  may  be  plunly  viable  to  the  naked  eye,  it  must  sub- 
tend an  angle  of  nearly  1'.  Consequently,  a  magnifying 
power  of  60  is  required  to  render  a  round  object  one  mile 
in  diameter  on  l£e  surface  of  the  moon  plainly  visible. 
Starting  firom  this  fact,  we  may  readily  form  the  follow- 
ing table,  showing  the  diameten  <A  the  smdlest  objects 
that  ean  be  seen  with  different  magnifying  powers,  always 
ft-jimtng  that  v&n<m  with  these  powers  is  perfect : 

Power     60 ;  diameter  of  object  1  mile. 
Power   160 ;  diameter  9000  feet. 
Power  600 ;  diameter  600  feet 
Power  1000  ;  diameter  800  feet 
Power  9000 ;  diameter  160  feet 

U  telaieo^  power  oonld  be  increased-indefinitely,  there 
woidd  of  oovnse  be  no  limit  to  the  minuteness  of  an  ob- 
ject TiriUe  OB  the  moon's  sorlaoe.  But  the  necessary 
lamtffMtiou  of  all  teksoopm  an  saoh  that  only  in  wtn- 
oi&iyeMaseMiMy  thing  be  gained  by  inersMiilg  <lie 


IkMMIB 


wimam 


MHM 


888 


ABTBOITOMY. 


magnif  jring  power  beyond  1000.  The  inflnenoe  of  warm 
and  cold  onrvnts  in  oar  atmosphere  is  such  as  will  for- 
ever prevent  the  advantageous  use  of  high  magnifying 
powers.  After  a  certain  limit  we  see  nothing  more  by 
increasing  the  power,  vision  becoming  indistinct  in  pro- 
ptxrtion  as  the  power  is  inoressed.  It  may  be  doubted 
whether  the  moon  was  ever  seen  through  a  telescope  to  so 
good  advantage  as  she  would  be  seen  with  a  magnifying 
power  of  600,  unaccompanied  by  any  drawback  from  at- 
mospheric vibrations  or  imperfection  of  the  telescope. 
In  <^er  words,  it  is  hardly  Ukely  that  an  object  less  than 
600  feet  in  extent  could  ever  be  seen  on  the  moon  by  any 
telescope  whatever,  unless  it  were  possible  to  mount  the 
instrument  above  the  atmosphere  of  the  earth.  It  is  there- 
fwe  only  the  great  features  on  the  surface  of  the  moon, 
and  not  the  minute  ones,  which  can  be  made  out  with  the 
telescope. 

GhatMtsr  of  the  lEooa'a  8nfflM».-^The  most  striking 
point  of  difference  between  the  earth  and  moon  is  seen  in 
the  total  absence  from  the  latter  of  any  thing  that  looks 
like  an  undulating  surface.  No  formations  (^lilar  to  our 
valleys  and  mountidn-ehains  have  been  detected.  The 
lowest  surface  of  the  moon  which  can  be  seen  with  the 
tdeseope  appears  to  be  nearly  cmootii  and  flat,  or,  to 
speak  more  exactly,  spheriesl  (because  the  nuNm  k  a 
sphere).  This  suiliwe  has  difhrent  shades  of  color  in 
dfiSerait  regiims.  Some  poitiouaniof  alft^t,  rilvery 
tint,  while  others  have  a  dark  gray  «|^peanuM6w  These  dif- 
fersnees  of  tint  seem  to  arise  from  (dKflsNUOMol  mateiiaL 

Upon  this  surfiMe  as  a  fouiiiitUm  ar»  bvilk  anmerous 
formationB  of  vartods siise%  b«t  dl  of  am^^ stmj^  ehar- 
aoter.  Their  geneval  fonn  esa  be  made  ool  by;  tt«  aid  of 
Fig.  88,  and  their  dinensionB  by  ^  soale^  ittifai  at 
tiie  bottwn  of  it  The  laigeet  and  meM  ptonddbttflnt 
leotues  are  known  as  craters.  They  have  a  ^jrpMl  fona 
wmwisHwg  of  a  rawid  or  onl  nuged  wall  iWiig  fropi Uto 
plane  in  the  mauMr  of  a  driSii*.  IMMmIIoii.. 


iii 


Theinflnenoe  of  warm 
ore  is  meh  m  will  for- 
se  of  high  magnifying 
B  see  nothing  more  by 
ming  indistinct  in  pro- 
It  may  be  doubted 
hrongfa  a  telesoope  to  so 
leen  with  a  magnifying 
any  drawback  from  at- 
ution  of  the  telescope, 
that  an  object  less  than 
sen  on  the  moon  by  any 
)  possible  to  moont  the 
ftheearth.  Itisthere- 
le  surface  of  the  moon, 
an  be  made  out  with  the 

00.— The  most  striking 
■rth  and  moon  is  seen  in 
of  any  thing  tihat  lodu 
'ormations  i^iilar  to  oar 
re  been  detwsted.  The 
h  can  be  seen  with  the 
smooth  and  flat,  or,  to 
beeanse  the  moon  is  a 
vent  shades  of  eolor  in 

15  are  of  atirii^t,  silvwy 
yippeanme^  These  dlf- 
m  dUEeraiees  of  matoiaL 
Bthm  are  built  BmaMrons 
dlof  a  tfif  simpte  ehar- 

16  made  oift  by,  tht  aid  of 
by  tlie  SQito^  fllEkn  at 
it  and  moM  pcomlnsnt 
They  have  a  typkal  f«m 


TUB  MOOITB  BUBFAGB. 


waUs  are  frequently  from  three  to  six  thoussnd  metres  in 
heif^t,  very  rough  and  broken.    In  their  interior  we  see 


lis.  A.— Mno*  or  na  mom's  somtmb. 

moen  lAraady  deseribed.    Itis, 
iHth  fwjguitfito  or  broken  «p 


1bk^fimtmxim»  of  the 
AuWllfei'i  gcMVi^  eofwad 


880 


ABTBONOMT. 


hj  small  inequalities  so  as  not  to  bo  easily  made  oat.  In 
the  oentre  of  the  craten  we  frequently  find  a  conical  for- 
mation rising  up  to  a  considerable  height,  and  much  larger 
than  the  inequalitieB  just  described.  In  the  craters  we 
have  a  vague  resemblance  to  volcanic  f ormati<Hi8  upon  the 
earth,  the  principal  difference  being  that  their  magnitude 
is  very  much  greater  than  any  thing  known  here.  The 
diameter  of  the  larger  ones  ranges  from  50  to  SOO  kilo- 
metres, while  the  smallest  are  so  minute  as  to  be  hardly 
visible  with  the  telescope. 

When  the  moon  is  only  a  few  days  old,  the  sun's  rays 
strike  very  obliquely  upon  the  lunar  mountains,  and  they 
cast  long  shadows.  From  the  known  po8iti<A  of  the  sun, 
moon,  and  earth,  and  from  the  measued  length  of  these 
shadows,  the  heights  of  the  mountains  can  be  calculated. 
It  is  thus  found  that  somoof  the  mountains  near  the  south 
pole  rise  to  a  height  of  8000  or  9000  metres  (from  9S,000 
to  80,000  feet)  above  the  general  surface  df  the  moon. 
Heights  of  from  8000  to  7000  metres  are  v«ry  common 
over  abnost  the  whole  lunar  suxfaoe. 

Next  to  the  so-called  craters  visible  on  the  lunar  disk, 
the  moet  curious  features  are  certain  long  bri^t  streaks, 
which  the  Germans  call  riUa  or  fmrmw.  These  extend 
in  l<mg  radiations  over  certain  of  the  craters,  and  have  the 
appearance  of  eraeks  in  tiio  lunar  surfaoe  which  have  been 
BubMquently  filled  by  a  brilliant  wliite  material  Na- 
sMtra  and  CAB^Bmaihave  deseribed  some  experiments 
detuned  to  ]m)duoe  this  appeanaw  aitiMatty.  They 
took  hdlow  ^ass  globes,  fiUedthem  irftli  water,  and  heat- 
ed them  untS  the  swiifle  waa  enusked.  IThe  oracka  gen- 
erated at  the  weakest  piiint  of  tkeioriMsenMJiate  fifon  the 
p<rfnt  in  a  manner  strOdngly  dmilariin  appeanaee  to  the 
riUs  on  the  moon.  It  wmdd,  however,  be  jwenkature  to 
conclude  that  the  latter  were  actually  iproduoed  in  this 
way. 

The  question  of  the  origin  of  the  lunar  features  has « 
bearing  on  theories  of  teriestrial  geology  as  well  as  upon 


'-"^■"UWiig 


easily  made  oat.  In 
lUy  find  a  conical  for- 
sight,  and  much  larger 
In  the  craters  we 
iC  formations  npon  the 

that  their  magnitude 
ig  known  here.  The 
from  60  to  aOO  kilo- 
inuteas  to  be  hardly 

lys  old,  the  sun's  rays 
r  mountains,  and  they 
m  poaitioi  of  the  sun, 
asmred  length  of  these 
ins  can  be  calculated, 
mntainsnear  the  south 
0  metres  (^m  95,000 
surface  df  the  moon, 
itres  are  vtry  oommon 

t)le  on  the  lunar  disk, 
in  long  bri^t  streaks, 
vrowt.  These  extend 
6  craters,  and  hare  the 
irf aoe  iHtioh  have  been 
white  material  Na- 
tbedsome  esperimrats 
BM  artlfldatty.  They 
iwlthwater,  andheat- 
kod.  5!beenidn  gen- 
uriMe  ndiato  from  the 
iriin  appeanuM  to  tbe 
ever,  be  pruilalwre  to 
nally  prodnoed  in  thia 

le  Innar  features  hM  * 
;eologyasw«U  as  upon 


LIGHT  AND  HBAT  OF  THB  MOON. 


Stl 


various  questions  respecting  tite  paafc  luatory  of  the  moon 
itself,  it  has  hmn.  awwidered  in  this  aspect  by  various 
geologista. 

Lunar  ▲tmomdiara. — ^The  question  whether  the  moon 
has  an  atmosphere  has  been  much  discussed.  The  only 
condnsion  which  has  yet  been  resohed  is  that  no  positive 
evidence  of  an  atmosphere  has  ever  been  obtained,  and 
that  if  one  exists  it  is  certainly  several  hundred  times  rarer 
than  the  atmosj^ere  of  our  eartL  The  most  delicate 
method  of  detecting  such  an  appendage  would  be  by  its 
refracting  the  light  of  a  star  seen  throu|^  it.  As  the 
moon  ad  vanoes  in  *  .onthly  course  around  the  earth,  she 
frequently  appears  to  pass  over  bright  stars.  These  phe- 
nomena are  called  ooou^to^MMM.  Just  before  the  limb  of 
the  moon  appears  to  reach  the  star,  the  latter  will  be  seen 
throu|^  the  moon's  atmosphere,  if  there  is  one,  and  will 
be  diq>laoed  in  a  direction  from  the  moon's  centre.  But 
the  most  careful  observations  have  failed  to  show  the 
sli^test  evidence  of  any  such  displacement.  Hence  the 
most  delicate  test  for  a  lunar  atmosphere  gives  no  evi- 
dence whatever  that  it  exists. 

The  speetra  of  stars  when  about  to  be  ooeulted  have 
also  been  examined  in  order  to  see  whether  any  absorption 
lines  which  m^^t  be  prodnoed  by  the  lunar  atmosphere 
became  visiUe.  The  evidence  in  this  direction  has  also 
been  negative.  Moreover,  the  spectrum  of  the  moon  itself 
does  not  seem  to  dlfEer  in  the  slightest  from  that  of  the. 
sun.  We  eonelude  tbarafol«  that  if  there  is  a  lunar  at- 
moepliere,  it  is  too  nra  to  exert  any  sensible  absoiption 
upon  the  rays  of  lijg^t. 

IdglitMiABMlorikfelleeai— Many  attempts  have 
been  made  to  measure  tbe  ratio  of  the  li^^t  of  the  full 
moon  Hid  tiial  of  the  nm.  The  results  have  been  veiy 
disowdwit,  but  att  have  agreed  in  showing  that  the  sun 
•mite  several  hundred  thousand  times  as  much  light  as  the 
fnllmooiit    Th« hwl  and  woit  careful  deterainatioft  is 


832 


ASTRONOMV. 


^ 


that  of  ZdLLRBR,  who  finds  the  sun  to  be  618,000  times  as 
bright  as  the  fnll  moon. 

The  moon  most  reflect  the  heat  as  well  as  the  light  of 
the  snn,  and  most  also  radiate  a  small  amoont  of  its  own 
heat.  But  the  quantities  thus  reflected  and  radiated  are  so 
minute  that  they  have  defled  detection  except  with  the 
most  delicate  instruments  of  research  now  known.  By  col- 
lecting the  moon's  rays  in  the  focus  of  one  of  his  large  re- 
flecting telescopes,  Lord  Bossi  was  able  to  show  that  a 
certain  amount  of  heat  is  actually  received  from  the 
moon,  and  that  this  amount  varies  with  the  moon's  phase, 
as  it  diould  do.  He  also  sought  to  learn  how  much  of 
the  moon's  heat  was  reflected  and  how  much  radiated. 
Thu  he  did  by  ascertaining  its  capacity  for  passing 
through  glass.  It  is  well  known  to  students  of  phyrics 
that  a  very  much  hu^r  portion  of  the  heat  radiated  by 
the  sun  or  other  extremely  hot  bodies  will  pass  throuj^ 
glass  than  of  heat  radiated  by  a  cooler  body.  Experiments 
show  that  about  86  per  cent  of  the  sun's  heat  will  pass 
through  ordinary  optical  glass.  If  the  heat  of  the  moon 
were  entirely  reflected  sun  heat,  it  would  possess  the  samo 
property,  and  the  same  {NPoportion  would  pass  through 
ghMB.  But  the  experiments  of  Lord  Bossk  have  shown 
that  instead  of  86  percent,  only  19  per  cent  passed  throufj^ 
the  glass.  As  a  general  remit  of  all  his  resoudies,  it  may 
be  supposed  that  about  six  sevenths  of  the  heat  given  out 
by  the  moon  is  radiated  and  one  seventh  reflected. 

Is  tkere  aaj  ekaaae  on  tte  muAm  of  tlM  Mtoonf— 
When  the  surface  of  the  moon  was  first  found  to  be  cov- 
ered by  craters  having  the  appeanmoe  of  voloanosa  at  the 
surface  of  the  earth,  it  waa  veiy  nalnrally  thoof^  that 
these  supposed  volcanoes  mig^t  be  itill  fai  activity,  and  ex- 
hibit themselves  to  our  teleaoopes  by  thev  flames.  Sir 
William  Hkbsohsl  supposed  that  ho  law  several  safih  vol- 
canoes, and,  on  his  authority,  they  were  "Umg  beBeved  to 
exist.  Snbeequent  obanrvations  have  ahown  that  tl^  was 
a  mistaken  opinion,  though  a  very  natural  one  under  the 


wmm 


\  to  be  618,000  timw  m 

M  well  M  die  light  of 
uUl  unonntof  its  own 
ctedand  radiated  are  bo 
ection  exoept  with  the 
«h  now  known.  By  ool- 
u  of  one  of  his  large  re- 
able  to  ihow  ^t  a 
illy  received  from  the 
with  the  moon's  pluwe, 
to  learn  how  much  of 
id  how  much  radiated. 
•  capacity  for  paning 
to  students  of  physics 
t  the  heat  radiated  by 
odieswill  pass  through 
>lerbody.    Experiments 
he  sun's  heat  will  pass 
f  the  heat  of  the  moon 
would  possess  the  samo 
ion  would  pass  through 
[jord  RossK  have  showu 
9  per  cent  passed  throuf^ 
all  his  resoudies,  it  may 
faa  of  the  heat  giren  out 
leventh  reflected. 
nuflMe  ct  tbm  Voenf — 
as  first  found  to  be  oot- 
■aaee  of  volcanoaa  aft  the 
y  naturally  thonglit  that 
e  Mill  in  activity,  and  ex- 
es by  tiieir  flaoMS.    Sir 
i  ho  law  aevend  •aflh  vol- 
)yw«re  long  beBevedto 
have  shown  that  this  was 
7  natural  one  under  the 


CttANOKS  ON  TBS  MOON. 


888 


clrcnmsUnoes.  If  we  look  at  the  moon  with  a  telescope 
when  she  is  three  or  four  days  old,  we  shall  see  the  darker 
portion  of  her  surface,  which  is  not  reached  by  the  sun  s 
rays,  to  be  faintly  iUuminated  by  Ught  reflected  from  the 
earth.  This  appearance  may  always  be  seen  at  the  right 
time  with  the  naked  eye.  H  the  telescope  has  an  aperture 
of  five  inches  or  upward,  and  thfB  magnifying  power  does 
not  exceed  ten  to  the  inch,  we  shaU  generally  see  one  or 
mora  spots  on  this  dark  hemisphere  of  the  moon  so  mudi 
brighter  than  the  rest  of  the  surface  that  they  may  well 
suggest  the  idea  of  being  self-luminous.  It  is,  however, 
known  that  these  are  only  spots  possessing  the  power  of 
reflecting  back  an  unusually  krge  portion  of  the  earth  s 
light.  Not  the  slightest  sound  evidence  of  any  incandes- 
cent eruption  at  the  moon's  surface  has  ever  been  found. 

Several  instances  of  supposed  changes  on  the  mowi's 
surface  have  been  described  in  recent  times.  A  few  yeais 
ago  a  spot  known  as  linnaus,  near  the  centre  of  the 
moon's  visible  disk,  was  found  to  present  an  appearance 
entirely  diilerent  from  its  representation  on  the  map  of 
Bran  and  Hakdlkr,  made  forty  years  b^ore.  More 
recently  Kltot,  of  Cologne,  supposed  himself  to  have  dis- 
covered a  yet  more  decided  ohaiige  in  anodwr  feature  of 
the  moon's  surface. 

The  question  wfaeTher  these  changes  are  provwi  is  one 
on  which  the  opinions  of  astroiu»nen  difler.  The  difficul- 
ty of  reaehing  a  oertain  oonohision  arises  from  the  fact  that 

each  leataie  nees»»ily  varies  in  appearance,  owingto  the 
dUlevent  ways  fai  which  the  sun's  light  falls  upon  it 
SomellmeB  the  changes  an  very  diflleult  to  account  for, 
even  whan  h  is  certain  that  they  do  not  arise  from  any 
dungeon  the  oMonitwlf.  Henee  while  some  regard  the 
apparent  ehaagea  as  real,  othen  regard^them  aa  due  only 
to  dilieienesa  in  the  mode  ol  iUamination. 


CHAPTER  V. 

> 

THE  PLANET  MABS. 
%  I.    DIBOBIFTIOir  or  TBM  VLAMWS. 

Mara  is  the  next  planet  beyond  the  earth  in  the  order 
of  distance  from  the  sun,  being  about  half  as  far  again  as 
the  earth.  It  has  a  decided  rad  color,  by  which  it  may 
be  readily  distinguished  from  all  the  other  planets. 
Owing  to  the  considerable  eccentricity  of  its  orbit,  its 
distance,  both  from  the  sun  and  from  the  earth,  varien  in  a 
larger  proportion  than  does  that  of  the  other  outer  planets. 

At  the  most  favorable  oppositions,  its  distance  from  the 
earth  is  about  0'88  of  the  astronomical  unit,  or,  in  ronnd 
numbers,  67,000,000  kilometres  (86,000,000  of  miles). 
This  is  greater  than  the  least  distance  of  Venutf  bat  we 
can  neverthelefls  obtain  a  better  view  of  Man  under  these 
circumstances  than  of  FmiM,  because  whm  the  lattor  is 
nearest  to  us  its  dark  hemisphere  is  turned  toward  us, 
while  in  the  case  of  Man  and  of  the  outer  planets  the 
hemisphere  turned  toward  ns  at  oppgsition  la  fully  illur 
minated  by  the  sun. 

The  period  of  revolution  of  Jfors  around  the  son  is  a 
little  leas  than  two  years,  or,  more  emetfy,  98/f  days.  The 
sueoessive  oppositions  oocmr  at  interrala  vi  two  yean  and 
(MM  or  two  months,  tlie  earth  having  made  duing  tiiia 
interval  a  little  more  than  two  nmAaiicm  mmmdilMnui, 
and  the  planet  Mara  a  little  more  than  one.  The  dates 
<^  sevend  past  and  future  oppoaitioiN  an  shown  in  the 
following  table : 


IfABS. 


the  earth  in  the  order 
mt  half  as  far  again  as 
>lor,  by  which  it  may 
ill  the  other  pUuiets. 
fcricity  of  its  orbit,  its 
m  the  earth,  varien  in  a 
the  other  outer  planets. 
IS,  its  distance  from  the 
nioal  unit,  or,  in  round 
(85,000,000  of  miles), 
woe  of  Vtnua,  but  we 
w  of  Man  under  these 
HUM  when  the  hitter  is 
)  is  turned  toward  us, 
the  outer  phmets  the 
if^positioii  is  folly  illu- 

r*  around  the  son  is  a 
e>«Qtfy^<)8?days.  Tho 
Mtals  of  tivo  yean  and 
liag  made  dwii^  this 
Dla^itHui  mmmdtJMmn, 
than  one.  The  dates 
ions  are  shown  in  the 


OPPOSmOlTB  OF  MARS. 

1871 March  20th. 

1878 April  27th. 

1876 June  20th. 

1877 September  6th. 

1879 November  12th. 

1881 DecomW  26th. 

1884 January  Slst. 

1886 March  6th. 


Owing  to  the  unequal  motion  of  the  planet,  arising  Aom 
the  eccentricity  of  its  orbit,  the  intervals  between  sue* 
ceosive  oppositions  vary  from  two  years  and  one  month  to 
two  years  and  two  and  a  half  months. 

About  August  26th  of  each  year  the  earth  is  in  the  sam6 
direction  from  the  sun  as  the  perihelion  of  the  orbit  of 
Mart.  Hence  if  an  opposition  occurs  about  that  time, 
Mar»  will  be  very  near  its  perihelion,  and  at  the  least 
possible  distance  from  the  earth.  At  the  opposite  season 
of  the  year,  near  the  end  of  February,  the  earth  is  on 
the  line  drawn  from  the  sun  to  the  aphelion  of  the  orbit 
Mar».  The  least  favorable  oppodtionB  are  therefore 
those  which  occur  in  February.  The  distance  of  Mam  is 
then  about  0*66  of  the  astronomical  unit. 

Tho  &vorable  oppositions  occur  at  intervals  of  15  t/t 
17  yean,  the  period  being  that  required  for  the  successive 
increments  of  <me  or  two  months  between  the  times  of  the 
year  at  which  successive  oppodtions  occur  to  make  up  an 
entire  year.  This  will  be  readily  seen  from  the  preceding 
taUe  of  the  times  of  opposition,  which  shows  how  the  op- 
poritioiis  nutgsd  trough  the  entire  year  between  1871 
and  188ft.  Thtt  opposition  of  1877  was  remarkably  fa- 
vorable. Hw  not  most  favoraUe  opposition  wHI  occur 
in  189». 

Mmt  WBBMnrny  eiidbits  phases,  but  they  are  not  s6 
w<^  muked  as  in Hm  owe  of  Vmui,  because  the  hani- 
tfkan  wljeh  it  {ffssents  to  the  obMrver  on  the  earth  is 
i4w»ys  mora  tim  half  illuminirted.    The  greatest  phase 


886 


ABTRomitr. 


oooun  when  its  direction  is  90°  from  that  of  the  «un,  and 
even  then  six  aeventha  of  its  diik  is  illuminated,  like  that 
of  the  moon,  three  days  before  or  after  full  moon.  The 
pliaaea  of  Mar$  were  observed  by  Galilko  in  1610,  who, 
however,  oould  not  describe  them  with  entire  certainty. 

BoUtion  of  Man.— The  early  telescopic  observers 
noticed  that  the  disk  of  Mara  did  not  appear  uniform  in 
color  and  brightness,  but  had  a  variegated  aspect  In 
1666  the  celebrated  Dr.  Bobut  Hookb  found  that  the 
maridngs  on  Mara  were  permanent  and  moved  around  in 
inoh  a  way  as  to  show  that  the. planet  revolved  on  its  axis. 
The  markings  given  in  his  drawing  can  be  traced  at  th« 
present  day,  and  are  made  use  of  to  determine  the  exaok 

Eiriod  of  rotation  of  the  planet.  Drawings  made  by 
mroHiNS  abont  the  same  time  have  been  used  in  tlM 
same  way.  So  well  is  the  rotation  fixed  by  them  that  the 
Mfcronomer  can  now  determine  the  exact  number  of  times 
the  pUmet  has  rotated  on  its  axis  since  these  old  drawings 
were  made.  The  period  has  been  found  by  Mr.  Pbooto* 
to  be  24i>  87"  32*>7,  *a  result  which  appears  certain  to  one 
or  two  tenths  of  a  second.  It  is  therefore  less  than  an 
hour  greater  than  the  period  of  rotation  of  the  earth. 

■nfftioe  of  Mars. — The  most  interesting  result  <tf  these 
nuurkiiigs  on  Mara  is  the  probability  that  its  surface  k  di- 
Tondfied  by  land  and  water,  ooverad  by  an  atmos^^ierB, 
and  altogether  very  similar  to  the  surface  of  the  earth. 
Some  portions  of  the  surface  are  of  a  dedded  red  ookM*, 
and  thus  give  rise  to  the  well>known  fioy  aspeei  of  tiie 
planet  Other  parts  are  of  a  greeniah  hue,  and  are  there- 
fore  supposed  to  be  seas.  The  meet  striking  features  are 
two  brilliant  white  regions,  one  lying  around  Mohpcd*  of  the 
planet  It  has  been  supposed  that  thia  appeeiwce  is  due 
to  immense  masses  of  snow  and  ioe  snrroukling  tiie  poles. 
If  thia  were  so,  it  would  indicate  thai  ^prooessea  of  evap- 
oiation,  doud  formation,  and  ewideneation  of  vapor  iiito 
lain  and  snow  go  on  at  tJie  turfaoe  of  Jf«rt  aa  at  the  snr< 
Imo  of  the  earOi.    A  certain  amount  of  color  is  given  to 


IqjI^! 


wm^^ 


rom  that  of  the  iun,  and 
is  illuminated,  like  that 
r  after  full  raoon.     The 
f  Galileo  in  1610,  who, 
I  with  entire  certainty, 
rly  telescopic    obaervera 
1  not  appear  uniform  in 
I  variegated  aspect.     In 
'  HooKB  found  that  the 
mt  and  moved  around  in 
lanet  revolved  on  its  axis, 
ing  can  be  traced  at  th« 
if  to  determine  the  exact 
St.     Drawings  made  by 
have  been  used  in  the 
on  fixedbythem  that  the 
lie  exact  number  of  times 
since  these  old  drawings 
>n  found  by  Mr.  Pbootob 
ch  appears  certain  to  one 
is  therefore  less  than  an 
rotation  of  the  earth, 
nteresting  result  of  these 
ility  that  its  surface  k  di- 
ivered  by  an  aimoKpbmPt 
the  surface  of  the  eurtli. 
d  of  a  dedded  red  ookv, 
oown  fieiy  nqteot  of  tiie 
eeniah  hue,  and  are  thero- 
most  striking  featurw  are 
ring  around  each  p(de  of  the 
lihet  thii  appeaivttoe  is  due 
ice  surrouk^ng  the  polfls. 
ithiKtIlieprooeiMt  oferap- 
Mmdensadon  of  vapor  into 
loe  of  Jf«rt  M  at  the  snr. 
uonut  of  eotoris  giveata 


ASP/ecr  OF  MARS. 


m 


tliitt  theory  by  supposed  uiiangus  in  the  inugiiitudu  uf 
tltuttu  icu-caps.  Uut  thu  prublunt  uf  eittablisliing  such 
changes  is  one  of  oxtromo  difficulty.  The  only  way  in 
which  an  ado<juate  idea  of  this  difficulty  can  be  formed  Is 
by  the  reader  himself  looking  at  Mara  through  a  telescope. 
If  he  will  then  note  how  hard  it  is  to  make  out  the 
difierent  slutdes  of  light  and  darkness  on  the  planet,  and 


"Si^mwmm 


how  they  must  vary  ill  aspect  under  different  oonditiims 
of  clearness  in  our  own  atmosphere,  he  will  readily  per- 
ceive that  much  evidence  is  necessary  to  establish  great 
changes.  All  wf,  o;.'.say,  tiierefore,  is  thai  the  formation 
of  tK«  ioe^saps  lu  v/inter  and  their  melting  in  summer  has 
some  evidence  in  its  favor,  but  is  not  yet  oompl^l|y 
provMi. 


■mKKim 


nnr 


838 


ASTRONOMT. 


g  2.    8ATBLUTBS  OF  MAB8. 

Until  the  year  1877,  Mar»  was  supposed  to  have  no  sat- 
ellites, none  having  ever  been  seen  in  the  most  powerful 
telescopes.  But  in  August  of  that  year,  Profeeeor  Hall, 
of  the  I)  aval  Observatory,  instituted  a  systematic  search 
with  the  great  equatorial,  which  resulted  in  the  discovery 
of  two  such  objects.  We  have  already  described  the  op- 
porition  of  1877  as  an  extremely  favorable  one ;  otherwise 
it  would  have  been  hardly  possible  to  detect  these  bodies. 
They  had  never  before  been  seen,  partly  on  account  of 
tiieir  extreme  minuteness,  which  rendered  them  invisible 
taoept  with  powerf^jl  instruments  and  at  the  most  favor- 
•I>le  ^imes,  and  partly  on  account  of  the  fact,  already  al- 
IlilkMito,  that  the  favorable  oppositions  occur  only  at  inter- 
vals of  15  or  17  years.  There  are  only  a  few  weeks  A\a- 
ing  each  of  these  intervals  when  it  is  practicable  to  distin- 
gnJah  them. 

These  satellites  are  by  far  the  smallest  celestial  bodies 
known.  It  is  of  course  impossible  to  measure  their  <Ham- 
elere,  as  they  appear  in  the  telescope  only  as  poiots  of 
Ii|g^t.  A  very  careful  estimate  of  the  amount  ol  fi^t 
tiHUeh  they  reflect  was  made  by  Professw  £.  C>  Floiun- 
no,  Director  of  the  Harvard  Ooll^^  Obaorwlory,  mho 
wJeulrted  how  large  they  ought  to  be  to  refleet  tt&i  ll|^t. 
%9  ttos  f<MUOKi  that  the  outer  satdlite  was  flvMtify  idSi»nt 
ii^  mUes  and  tiie  inner  one  about  wesvmiaSim  te  (Jltmillwr, 
impfioAux  them  to  Msfleok  the  Mbifiiiv^fitdMljr  «i  Jlin 
(MM.  The  <Hiter  one  wm  mbh  «m  #^  lelnQope  al « IHi- 
tanoe  from  the  earth  of  7,000,000  thnei  tiiis  diameter. 
The  proportion  woukk  be  that  <tf  a  baB  two  inohei  fa  di- 
ameter  viewed  at  a  distanoe  isqiud  to  that  faetween  tlM 
oHies  of  Boston  and  Kew  YoA.  Snehaifeat  of  tdeaeoph 
seeingiB  well  fitted  to  give  an  ideaof  tlia  power  of  modem 
optiod  instmmeDta. 

Professor  Hall  found  that  ^  onler  ntdllfa,  iriiiel 
he  called  JMmoty  revdvea  jronnd  thai  planet  Itt  9^  UPP, 


^'^^^^m^mm^'v^mM-rnhki'mi 


fT. 


I  OF  MABS. 


s  supposed  to  have  no  sat- 
en  iu  the  most  powerful 
bat  year,  Profeeeor  Hall, 
;uted  a  systematic  search 
resulted  in  the  discovery 
already  described  the  op- 
favorable  one  ;  otherwise 
)le  to  detect  these  bodies, 
sen,  partly  on  account  of 
\  rendered  them  invisible 
its  and  at  the  most  favor- 
int  of  the  fact,  already  al- 
witions  occur  only  at  inter- 
ire  only  a  few  weeks  d^r-- 
L  it  is  practicable  to  distin- 

B  smallest  celestial  bodies 
ble  to  measure  their  ^Kam- 
iescope  only  as  pointa  of 
)  of  the  amount  ol  lii^t 
y  Professor  £.  0.  tmxa.- 
Oollef^  Observiiory*  who 
t  to  be  to  reMi  &}«  li#it. 
iteQHe  waa  fi«i«bfy  i^ut 
nt  seven  v^oi  fat#uniiier, 

Asm  n^fnOm^  m  J^ 
wi1ii^tilMQ0pe«l*iiB- 
1,000  timei  tills  diameter, 
of  a  bail  two  inohai  ftt  di- 
lepuX  to  that  .between  Hio 
:.  8aeh«feat  of  teleaeopic 
toiof  tlis  power  of  modern 

Hm  onier  aatelMi^  uMi 


SATELLITSa  OF  MARS. 


339 


and  the  inner  one,  called  Phcloa,  in  7**  38*".  The  latter  is 
only  5800  miles  from  the  centre  of  Mare,  and  less  than 
4000  miles  from  its  surface.  It  would  therefore  be  almost 
possible  with  one  of  our  telescopes  on  the  surface  of  Mar» 
to  see  an  object  the  size  of  a  large  animal  on  the  satellite. 
This  diort  distance  and  rapid  revolution  make  the  inner 
satellite  of  Mars  one  of  the  most  interesting  bodies  with 
which  we  are  acquainted.  It  performs  a  revolution  in  its 
orbit  in  less  than  half  the  time  that  Mars  revolves  on  its 
axis.  In  consequence,  to  the  inhabitants  of  Mars,  it 
would  seem  to  rise  in  the  west  and  set  in  the  east  It  will 
be  remeral)ered  that  the  revolution  of  the  moon  around 
the  earth  and  of  the  earth  on  its  axis  are  both  from  west 
to  east ;  but  the  latter  revolution  being  the  more  rapid,  the 
apparent  diurnal  motion  of  the  moon  is  from  east  to  west. 
Iu  the  case  of  the  inner  satellite  of  Mars,  however,  this 
is  reversed,  and  it  therefore  appears  to  move  in  tl  e  actual 
direction  of  its  orbital  motion.  The  rapidity  of  ix.'  phases 
is  also  equally  remarkable.  It  is  less  than  two  hours  from 
new  moon  to  first  quarter,  and  so  on.  Tlius  the  inhabit- 
ants of  Mars  may  see  tlieir  inner  moon  pass  through  idl 
its  phases  iu  a  single  night 


L 


tmmmimimatm 


CHAPTER  VI. 

THE  MINOR  PLANETS. 

Whkn  the  solar  system  was  firet  mapped  out  in  its  trne 
proportions  by  Copbeniccs  and  Kkplkb,  only  six  primary 
planets  were  known  —  namely,  Merowry,  Vemu,  the 
£arth,  Mars,  JvpUery  and  Saium.  These  suooeeded 
each  other  according  to  a  nearly  regnkr  kw,  as  we  have 
shown  in  Chapter  I.,  except  that  between  Mars  and  .AipH 
fer  a  gap  was  Icrft,  where  an  additional  pknet  might  be 
inserted,  and  the  order  of  distance  be  thns  made  complete. 
It  was  therefore  snpposed  by  the  astronomers  of  the  seven- 
teenth  and  eighteenth  centuries  that  a  planet  might  b^ 
found  in  this  region.  A  search  for  this  object  was  insti- 
tuted toward  the  end  of  the  last  century,  but  before  it 
had  made  much  progress  a  planet  in  the  place  of  the  one 
so  long  expected  was  found  by  Pia«m,  of  Palermo.  The 
discovery  was  made  on  the  first  day  of  the  pvesent  century, 
1801,  January  Ist. 

In  the  couree  of  the  foHowing  seven  yean  the  astronom- 
ical worid  was  surprised  by  the  discovery  of  tiiree  othei 
planets,  all  in  the  same  region,  though  not  levolviag  m 
the  same  orbits.  Seeing  four  small  planeto  where  on< 
huge  one  ought  to  be,  Olbhbs  was  led  to  hi»  eelebwtec 
hypothesis  that  ^msm  bodies  were  the  fn«meiits  of  a  la>g( 
planet  which  had  been  broken  to  pieeea  by  the  aetkm  a 
some  unknown  f<Nroe. 

A  generation  of  astronomen  now  passed  imr^  ^^^ 
,the  discovery  of  more  Aan  these  four.    But  in  0        ^^ 
1846,  Hrhokk,  of  Dreisen,  being  engeged  Hi 


■MFfMMM 


^  VI. 

LANB'rS. 

rrt  mapped  ont  in  its  trae 
Kbpleb,  only  six  primary 
,  Mercury  t  Venus,  the 
Uum.  Theee  suooeeded 
'  regular  law,  as  we  have 
I;  between  Mars  and  Jvpi- 
Iditional  planet  might  be 
se  be  thus  made  complete, 
astronomen  of  the  seven* 
»  that  a  planet  might  }y* 
for  this  object  was  insti- 
ast  oentnry,  bat  before  it 
et  in  the  place  of  the  one 
Puzu,  of  Palermo.  The 
day  of  the  praamt  century, 

^  seven  yean  tiie  astrcmom- 
)  discovery  d!  tiiree  other 
k,  thoii(g^  not  nvolvii^  m 
small  planets  where  one 
was  led  to  his  eelebnited 
ire  the  fragmeRts  of  a  laige 
to  pieces  by  the  Mtkm  oi 

now  passed  «wn/  without 
lefoar.  Bntir.  Doeenhpr, 
)eing  engaged  in  manptng 


THB  MINOR  PLANETS. 


841 


down  the  stars  near  the  ecliptic,  fonnd  a  fifth  plauot  of 
the  group.  In  1847  three  more  were  discovered,  and 
discoveries  have  since  been  made  at  a  rate  which  tlius  far 
shows  no  signs  of  diminution.  The  number  lias  now 
reached  200,  and  the  discovery  of  additional  ones  seems  to 
be  going  on  as  fast  as  ever.  The  frequent  announcentents 
of  the  discovery  of  planets  which  appear  in  the  public 
prints  all  refer  to  bodies  of  this  group. 

The  minor  planets  are  distinguished  from  the  major 
ones  by  many  characteristics.  Among  these  we  may 
mention  their  great  number,  which  exceeds  that  of  all  the 
other  known  bodies  of  the  solar  system  ;  their  small  size ; 
their  positions,  all  being  situated  between  the  orbits  of 
J^<ir«and  JvpUer;  the  great  eccentricities  and  inclina- 
tions of  their  orbits. 

number  of  Small  Planets. — It  would  be  interesting  to 
know  how  many  of  these  planets  there  are  in  all,  but  it  is 
as  yet  imposdble  even  to  guess  at  the  number.  As 
alrouly  stated,  fully  IKK)  are  now  known,  and  the  number 
of  new  ones  fonnd  eVery  year  ranges  from  7  or  8  to  10  or 
12.  If  ten  additional  ones  are  fonnd  every  year  during 
the  remainder  of  the  oentnzy,  400  will  then  have  been 
discovered. 

The  disoovery  of  these  bodies  is  a  v^  difficult  work, 
requiring  great  jwactioe  and  skill  on  the  part  of  the  as- 
tronomer. The  difficulty  is  that  of  distinguishing  them 
amongst  the  hnndreds  of  thousands  of  telescopic  stars 
which  are  scattered  in  the  heavens.  A  minor  planet 
presents  no  sensible  disk,  and  therefore  looks  exactly  like 
a  small  star.  It  can  be  detected  <mly  by  its  motion  among 
Lhe  sommnding  stan,  which  is  so  slow  that  hours  or  even 
days  must  ebpse  before  it  can  be  noticed. 

liH(BitadM.-^In  oonsequenoe  of  the  mmor  pknets  hav- 
ixig  no  visible  disks  in  the  most  powerful  telescopes,  it  is  im- 
pMsible  to  make  any  precise  measurement  of  their  diam- 
•Ian.  These  can,  however,  be  estimated  by  the  amount 
M  fisht  which  the  planet  rejlects.    Supposing  the  propot- 


849 


ASTRONOMY. 


tion  of  light  reflected  about  the  same  as  in  the  ease  of  the 
lai^r  planets,  it  is  estimated  that  the  diameters  of  the 
three  or  four  largest,  which  are  those  first  discovered, 
range  between  300  and  600  kilometres,  while  the  smallest 
are  probably  from  20  to  50  kilometres  in  diameter.  The 
average  diameter  of  all  that  are  known  is  perhaps  less  than 
150  kilometres — that  is,  scarcely  more  thaii  one  hundredth 
that  of  the  earth.  The  volumes  of  solid  bodies  vary  as  the 
cubes  of  their  diameters ;  it  might  therefore  take  a  million 
of  these  planets  to  make  one  of  the  size  of  the  earth. 

TOrm  of  Orbita.-~The  orbits  of  the  minor  plairata  are  much 
mora  eccentric  than  thoae  of  the  hrger  ones ;  their  distiince  from 
the  sun  therefore  raries  venr  widely.  The  most  eccentric  orbit  jet 
known  is  that  of  AMm,  which  was  discovered  by  Professor  Wat- 
soM  in  1878.  Its  least  distance  from  the  sun  is  I'Al,  a  very  little 
further  than  JTort,  while  at  afriielion  it  is  8 -59,  or  more  than  twice 
as  far.  Two  or  three  others  are  twice  as  far  fnnn  the  son  at  aphe- 
lion as  at  perihelion,  while  nearly  all  are  so  eccentric  that  if  the 
orlnts  were  drawn  to  a  scale,  the  «ye  would  readily  pero^e  that  the 
sun  was  not  in  their  centres.  The  largest  incUiumon  of  all  is  that 
of  PMu,  which  is  one  of  the  original  four,  hairinff  been  discovered 
by  OLBUia  in  180S.  The  inclinimon  to  the  eeHpoe  is  S4%  or  more 
than  one  third  of  a  r^t  angle.  Five  or  six  others  have  ineUaations 
exceeding  M*;  they  therefore  range  eatireW  outside  the  lodiae,  and 
in  fact  sometimes  culminate  to  the  north  of  our  aenlth. 

CMgin  of  tlMlUiior  Flail0ta.--The  question  <rf  the  ori|^n  of 
these  bodies  was  long  one  of  great  interest  The  features  which  we 
have  described  associate  themselves  veiy  naturally  with  the  oel»- 
brated  hypothesb  of  OLana,  that  we  here  hava  the  Aiagaasirta  of  a 
single  Inge  planet  which  in  the  beginning  revolved  in  its  proper 
phwe  between  the  orblu  of  Jftr*  ana  J^pitir.  Qusaa  Umsetf  siw- 
1  a  test  of  his  theory.    If  these  bocBea  were  raally  ftmned  hj 

rtoaioB  of  the  kige  one,  the  sepante  oitilB  of  the  frsgrneats 
all  pass  through  thejpoiiit  where  tiw  «qpIoaioa  occurred.  A 
comown  pdnt  of  intersectfen  was  tbenfore  hmg  looked  for ;  but 
although  two  or  three  of  the  first  foor  did  maa  vnMj  asar  each 
oAer,  the  required  point  ooold  not  be  f oond  for  all  four. 

It  waa  then  sugested  that  the  secular  chaiwes  in  the  oiMts  pro- 
duced by  tiie  aettmi  <rf  the  other  phuieti  would  in  tiiM  diatMe  the 
Crftiona  tS  all  the  orMts  in  saeh  a  way  ttat  thqr  woald  ao  {eager 
TeatqreoauaoQiateneeUoo.  The  seenlarvarlanoBs<rf  their  omts 
weretiMrdioneoBsputed,  tosee  if  thero  waaacyaignof  the  reqidred 
intersection  in  past  sges,  but  bow»  couM  be  found.  Ko  support 
has  beea  gtvea  to  Olbbbs*  hypothesis  by  aubsoqunt  fanresti|atioBS, 
and  it  is  ao  hwger  considered  by  aatranooMn  to  have  any  founda- 
tioB.  00  Iv  as  cui  be  judged,  these  bodies  have  been  remrfviMr 
arovud  uie  sua  as  separate  paaets  ever  siaoe  the  aofav  systwa  itaNl 
was  fomed. 


aa^eapli 
woulai 


me  RB  in  the  case  of  the 
Eit  the  diameters  of  the 

those  first  discovered, 
letres,  while  the  smallest 
letres  in  diameter.  The 
lown  is  perhaps  less  than 
Qore  than  one  hundredth 
:  solid  bodies  vary  as  the 

therefore  take  a  million 
:e  size  of  the  earth. 

he  minor  plaiMta  are  much 
r  ones ;  their  diatiuiM  from 
The  most  eccentric  orbit  jet 
scovered  by  Prof ewor  Wat- 
he  sun  is  1*61,  s  very  little 
it  is  8*60,  or  more  than  twice 
as  far  from  the  son  at  aphe- 
am  so  eccentric  thatif  tlie 
Mild  readily  pera^e  tliat  the 
rest  inclimmon  of  all  is  that 
four,  having  been  discovered 
D  the  eettpoe  is  84%  or  more 
*  six  others  have  inetiBations 
tirelv  outside  the  ndiao,  and 
^  m  our  Muith. 
he  queatfou  <rf  the  origin  of 
rest  The  fsatnna  which  we 
rery  naturally  with  the  cele- 
here  have  tte  in«MBts  of  a 
uin^  revolved  in  its  propw 
vfUtr.  OUBM  himself  mm- 
lodiet  wen  really  formed  1^ 
HUte  oibito  of  tile  ftagmeats 
a  tiie  exnloaioB  occurred.  ▲ 
mf ore  long  looked  f ov ;  but 
or  did  pH«  wettyMsr  eadi 
fooad  for  all  four.  ^^ 
ar  cha^eaiathe  oiMtapn>> 
m  wouu  fai  time  eharae  tho 
ly  tiMt  thqr  would  no  lennr 
eular  vailatloBs  of  tMr  oiwts 
B  wa«  acy  ^gn  ^  the  requlrad 
ottld  be  fonnd.  Bo  sap|mFt 
Iqr  subsemwrt  investJaaaoy, 
moaanto  have  anyfoundap 
bodies  have  hem  *«*<>^[^ 
r  siM»  the  sohw  aystsm  UsaB 


CHAPTER  VII. 

JUPITER  AND  HIS  SATELLITES. 

§  1.  THB  YiJkSws  nrevasBL. 

Jupiter  is  mnch  the  largest  planet  in  the  system.  His 
mean  distance  is  nearly  800,000,000  kilometres  (480,000,- 
000  miles).  His  diameter  is  140,000  kilometres,  corre- 
sponding to  a  mean  apparent  diameter,  as  seen  from  the 
snn  of  86' .  6.  His  linear  diameter  is  about  ^^  his  surf  aqe 
is  flvy  and  his  volume  xhv  ***•*  ®*  *^®  ■""•  ^^  "»■»  i« 
J™,  and  his  density  48  thns  nearly  the  same  as  the  ana**— 
v£,0.»4oftheearth'B.  Herot«te8onhia«xi«hi»»6ft-a0*. 

He  fa  attended  by  four  satellites,  whidi  wore  diwovend 
by  Oaulso  <m  JanuMy  Tib,  1610.  He  named  then  in 
honoroftheM»Diois,theJfo*fo«m«tor#.  These  sateffites 
were  independently  discovered  on  January  16th,  1610,  by 
HAsnor,  of  England,  who  observed  them  through  several 
subsequent  yeaifc  Smow  Mawos  al«o  appeaw  to  have 
eariy  obeerved  tlwm,  and  the  honor  of  their  disoovery  m 
cUtimed  for  him.  They  are  now  known  as  Batelhtes  I, 
II,  III,  and  rV,  I  being  the  nearest. 

The  surface  of  JvpiUr  has  been  carefully  studied  with 
the  tekicope,  pe-ticukriy  within  the  p«it  20  years.  Al- 
though further  from  ua  than  Jfow,  the  details  of  his  disk 
aie  hiueh  earier  to  wcogniae.  The  most  charactenstic 
featnwB  are  given  in  the  drawings  appended.  These  feat- 
ures are,  i8r^,  the  dark  bands  of  the  equatorial  ryons, 
and,  a^wmay,  the  cbnd-like  forms  spread  overneariyUie 
wfa^iaoifaoe.    Atthelimballtheaedetaihbeeomemdis- 


imiWIIili 


J 


AarHONOMY. 

tinct,  and  finally  vanish,  thus  indicating  a  highly  absorptivo 
atmosphere.  The  light  from  the  centre  of  the  disk  is  twice 
aa  bright  as  that  from  the  poles  (Akaoo).  The  bands  can 
be  seen  with  instruments  no  more  powerful  than  those 
used  by  GALtuto,  yet  he  makes  no  mention  of  them,  al- 
though they  were  seen  by  Zuocni,  Fontama,  and  others  be- 
fore 1638.  HinvHKNS  (1659)  describes  the  bands  as 
brighter  than  the  refiA  of  the  disk — a  unique  observation, 
on  which  we  must  look  with  some  distrust,  as  siitce  1660 
they  have  constantly  been  seen  darker  than  the  rest  of  the 
planet. 

The  color  of  the  bands  is  frequently  described  as  a  brick- 
red,  but  one  of  the  authors  has  niade  careful  studies  in 


•— TBunnopio  vnnr  or  nmm  ukd  m  «a< 


ool<»  of  tUi  planet,  and  finds  the  prevaiUng  tint  to  b0  a 
wtkuoxk  oolbr,  exactly  similar  to  the  odior  of  JVorv.  >  Tbe 
position  of  the  bands  varies  in  latitude,  and  the  shapes  of 
the  limiting  curves  also  change  from  day, to  day  ;  but  in 
the  nuun  they  nmaan  as  permuient  features  of  the  region 
to  which  they  belong.  Two  such  bands  are  usually  vis- 
Able,  but  often  mmre  are  seen.  For  eitam^e,  Oassidi 
(1690,  December  16th)  saw  six  parallel  ba&ds  extending 
completely  anmnd  the  planet.  HutsbaKL,  in  the  yeair 
1798,  attributed  iStta  aspects  of  the  bands  to  zones  of  the 
planet's  atmoqdiiero  more  tran<^il  and  less  filled  vl^ilh 
doads  than  ^  rerauning.  parnbns,  so  as  to  permit  the 


§IIWJiiSi»WWmW»i^^ 


r. 

lating  a  highly  uheorptive 
iontre  of  the  disk  is  twice 
Ikago).  The  bands  caii 
»re  powerful  tlian  those 
no  mention  of  them,  al- 
FoNTANA,  and  others  be- 
describes  the  bands  as 
■a  unique  observation, 
le  distrust,  as  since  1660 
rker  than  the  rest  of  the 

ntly  described  as  a  brick* 
made  careful  studies  in 


noi  Axommtti 


e  imvittUng;  tint  to  be  a 
yhe  color  of  JViir*.  >  ThA 
bitnde,  and  the  pluipes  of 
■om  day.to  day  ;  but  in 
at  features  of  the  region 
1  bands  are  usually  tis- 
For  example,  Oassh^ 
parallel  ba&dfi  extending 
HsBsbBKL,  in  the  yea^ 
e  bands  to  zones  of  the 
lil  and  lew  filled  #ith 
sns,  so  as  to  permit  the 


A8PE0T  OF  JUPITBR. 


845 


true  surface  of  the  phmet  to  bo  seen  tlirongh  these  zones, 
while  the  prevailing  clouds  in  the  other  regions  give 
a  brighter  tint  to  these  latter.  The  color  of  the  bands 
seems  to  vary  from  time  to  time,  and  their  bordering 
lines  sometimes  alter  with  such  rapidity  as  to  show  that 
these  borden  are  formed  of  something  like  clouds. 

The  clouds  thenuelveB  can  easily  be  seen  at  times,  and 
they  have  every  variety  of  shape,  sometimes  appearing  as 


BAVMU&nS'AXP 

biQIisiit  draW'^iHetnasses,  but  oftenerthey  are  rimilar 
in  f  <«ic  k>  a  scilb  of  white  eanmlons  clouds  such  as  are 
ib^qoently  seen  pQed  up  new  tiie  horiison  on  a  rammer's 
day.  Dm  twadi;  ^emselvei  seon  fre^riiratly  to  be  veiled 
over  with  solnelliili(  Vice  ^  thin  omtm  donds  of  onr 
stmoii^^  On  <Mi«  oeeisiofi  an  ammlns  of  white  eloud 
i^sMtt^  OM  lill^  diurk  bands  lor  many  days,  retain' 
lag  its  fll^qpe  liidraiq^  ^  whole  period. 


346 


A8TR0N0MT. 


Snch  donds  can  be  tolerably  accurately  obeerved,  and 
may  be  used  to  determine  the  rotation  time  of  the  pknet. 
These  obeervatiouB  show  that  the  clouds  have  often  a 
motion  of  their  own,  which  is  also  evident  from  other  con- 
siderations. 

The  following  results  of  observation,  of  spots  situated  in 

various  legions  of  the  pUmet  will  illustrate  this  : 

I 

h.  m.  *> 

Gamimi.... WM,    roUtloBUii»  =  »  S6  00 

HUMOBU. 17TB,  ••     =9  SS  40 

HnnoHBt. Vm,  •«     «  0  80  48 

BoBKonwi. i«5.  ••    Bf  «•  ae 

Bbui*M1oucb....    1888.  "b  8   85   88 

A»T 1888.         "         ••     =  8    86    81 

BoBXiiyr 1888,        "        •'     =  8   88   » 


%  2.    TEQi  flATKiUnm  OT  JUFITMR. 

MottonaoftlMtet^UitM.-'The  four  satellitei  move 
about  JufiUer  from  west  to  east  in  nearly  ciroubr  <nMti. 
W2ien  one  of  these  satellites  passes  between  tlie  nm  mm! 
JupUefy  it  easts  a  shadow  upon  Jvpiter'*  disk  ^  Fig.  98) 
preeiaely  a*  the  shadow  of  our  moon  is  thrown  upon  the 
earth  in  a  solar  edipee.  If  the  satellite  paam  tbiMtth 
JupUer't  own  shadow  in  its  revolntiooi,  an  ipdfpae  of  tUa 
satelUte  takes  plaoe.  H  ft  pMaes  betireea  the  eMIli  and 
/«^A^,  it  iapiojeeted  upon  .^itfwM«  dUc*  and  m  han  » 
tranrit ;  if  JvpUtr^B  between  the  earth  ud  the  saidfite, 
an  occultation  of  the  latter  oooois.  All  theae  phenomena 
can  be  seen  from  the  earth  with  a  oonun<m  tdeaeope,  and 
the  timeaof  observation  are  all  found  predicted  in  the 
Naiuticdl  Almanae.  In  this  way  we  aie  sure  that;  the  black 
spots  which  we  see  movii^  across  the  .disk  of  JvjpUer  ai« 
really  the  shadows  of  the  satel^tee  ttouwlvee,  and  not  phe- 
nomena to  be  otherwise  ezplaiaed.  These  shadow*  being 
seen  blaok  npon  J^ipUer^t  warfMoe,  show  tint  this  planet 
synes  by  reflecting  the  li^t  of  the  snn. 


msmms^mmmmmm 


Mjurately  observed,  and 
tion  tiiue  of  the  planet, 
e  clouds  have  often  a 
evident  from  other  con- 

iion,  of  spots  situated  In 

Uustrate  this : 

I 

A.  m.  A 

OB  tlms  =  9  fi6  00 

••     =  9  5S  40 

"     s  9  90  48 

»     B  t  M  86 

••     B  9  85  M 

•'     s  9  89  91 

••     z=  9  89  » 


OF  jurmttL 

e  four  satellitea  move 
nearly  cironlar  orbits. 
IB  between  tin  ran  and 
piW'«disk^Fig.98) 
Mm  is  thrown  npon  the 
satellite  panes  tiWMtth 
Btiom,  an  9clipie  of  ttja 
I  befeireen  the  eerth  and 
E«r*«  4Uki  mi  we  have  a 
I  earth  and  the  satellite, 
All  these  phenomene 
oomuMm  tdeseopOf  and 
found  predicted  in  the 
re  are  sure  that;  the  black 
tiie.disk  of  Jiipiier  are 
Itonnlves,  and  not  phe- 
.  3%ase  shadows  befaig 
e,  show  tin*  this  planet 
le  sun. 


SATKLLITBa  OF  JUPITBR. 


847 


lUeaoopio  Appeaianoe  of  the  teteUites.— Under  ordi- 
nary circumstances,  the  satellites  of  JupUer  are  seen  to 
have  disks— that  is,  not  to  be  mere  points  of  light.  Un- 
der very  favorable  conditions,  markings  have  beeen  seen 
on  these  disks,  and  it  is  very  curious  that  the  anomalous 
appearances  given  in  Fig.  98  (by  Dr.  Hastimos)  have  been 
iteen  at  various  times  by  other  good  observers,  as  Sboohi, 
LHwKs,  and  RtrruKuruRD.  Satellite  III,  which  is  much 
the  '^rgest,  has  decided  markiny  on  iU  faoe ;  IV  some- 
times app?4n,  as  in  the  figui,  to  have  iti  eiroolar  oatUne 


Fni.98, 


trrmtmntiM  or  nrmai's  satbixrMi 


cut  o£E  by  right  lines,  and  sajPlte  I  sometimes  appears 
gibbous.  The  opportnaWes  for  observing  these  q>pear- 
ances  are  so  laie  that  v/lifm$  h  known  beyond  the  Iwe 
fact  of  their  existence,  ui/i  Ho  |bnsiUe  explanation  of  the 
figure  shown  in  IV  haa  tecnjNn- 

^EMaSil^Slli-^MWlSliMHiH  :fUIs  «Ms'tai«Mi'to 


MMMMiaS^tesI  '^SSrmm  tlw''astttd  Haat  diMni'froai 
ii*?"!S!iT  iKnmi  W^  -^R difll-f  sdgss  of  ttas flaMl  and 
SiStoralSisi  «lotatAm  the  oelliass  of  the 

•'^'iiSSlidwthe  Doritkm  of  J^yitormsfkid/tothslrft 
of  th.  tg«^  It  l«4iig  ihenlnwiiiodtfcm  to  tbM^^ 

on  the  tSrtli  at  FoSdd  -o*  t^  «•  ?^**^wI7S  JL2f 
rtukUm of .?i»«<r !»««« ti«ktt« to  wtiw^ 

Hraoa.  as  th?«tdllto -owsawaad,  bewttlses  i^^^^Pf*^j°«^ 
grtOliSto  the  oAto  «tf  ^M**"  to  »  g»«*  thrt  it  soMsthw- «--» 


— xw-w^wpppiPHBn 


■t 


348 

entirelj  »bove  or  bvlow 
ktall. 


ASTRONOJIir. 
the  planet,  and  therefore  U  nut  occulted 


I^et  us  next  conaider  Jupiter  in  the  noaition  J"  near  the  bottom  of 
the  figure,  the  shadow,  aa  before,  pointing  from  the  planet  directly 
away  from  the  sun.  If  the  shadow  were  a  visible  object,  the  ol>- 
•erver  on  the  earth  at  T  could  see  it  projected  out  on  the  right  of 
the  f 'wet,  because  he  is  not  in  the  line  between  Jupiter  and  the  sun. 
BcBce  aa  a  satellite  moves  around  and  enters  the  shadow,  he  will  sec 
it  disappear  from  sight,  owing  to  the  sunlight  being  cut  off ;  this 


ti  called  an  eMpm  Ht^fmnmrn.  If  tbe  iitalllto  k  oqe  «r  the  two 
outer  oDon,  he  wiU  be  aUe.  to  see  K  vrnffrnf  agaia  after  it  oomea 
oak  of  the  shadow  befora  it  ia  ocevHed  brtriad  tte  pkMt 

Boob  afterwafd  theocoiiUatioft  wttl  oeow,  Md  it  wfll  afterward 
reaniaw  oa  the  left  In  the  ean^tiwl«Mrior;iMtiilellifo,  bow- 
ever,  tho  point  of  ensigenee  tmm  tke  Omitm  iahMden  behM  the 
planeMonaeqnettllytheobeervwv  after  itoswtdlwmi^ 
ow,  iiffl  net  aee  it  ie«Mpear  until  it  enenMa  fkoMl^d'OMrplMet 

IftbeplMetiaiBtle  peiitioni^,tiMarttiliftewffl  be  oeoSted 


SATKLLlTSa  OF  JUPJTAJt. 


340 


therefore  ia  nut  occulted 

ition  J"  near  the  bottom  of 
ng  from  the  planet  directly 
re  a  visible  object,  the  ol>- 
>jected  out  on  the  right  of 
Btween  Jvpiter  and  the  sun. 
ten  the  anadow,  he  will  see 
mlight  being  cut  off ;  thia 


I  *ttliU*  fa  oqe  of  the  two 
ipfMr  uaia  aft*  it  cooMa 
teldad  flwnkaet 
«owr,;aMl  ft  wffl  aftermrd 
lumionintmuimd.  how- 
nimR  b.liid(l«i  bebM  tba 

BM.InMaliM^  tha,pi««t 
'MtaUitaifiU  iM  omSed 


behind  the  planet  where  it  roarhea  tlio  first  dut(  '-d  linn.  If  it  ia  the  in- 
ner aatellite,  it  will  not  be  been  to  reapptiar  on  the  other  aide  of  the 
planet,  because  when  it  reaches  the  aecond  dotted  line  it  haa  entered 
the  ahadow.  After  a  while,  however,  it  will  reappear  from  the 
ahadow  aoine  little  distance  to  the  left  of  the  planet ;  thia  phe- 
nomenon ia  railed  an  eelipte  reoftpearonee.  In  the  caae  of  the  outer 
aatellitea,  it  may  aometimoa  hapnen  that  they  are  viaible  for  a  abort 
time  after  they  emerge  from  benind  the  diak  and  before  they  enter 
the  ahadow. 

Theae  different  appearances  are,  for  convenience,  repreaentod  in 
the  figure  aa  correaponding  to  different  poaitiona  of  JuvUtr  in  his 
orbit,  the  earth  having  the  aame  poaition  in  all ;  but  since  JvfUer 
revolves  around  the  sun  only  once  in  twelve  years,  the  changes  of 
relative  positioto  really  correspond  to  different  positions  of  the  earth 
in  its  orbit  duriof '  '  he  course  of  the  year. 

The  satellites  cuiupletely  disappear  from  telescopic  view  when 
they  enter  the  shadow  of  the  planet.  Thia  seems  to  show  that 
neither  planet  nor  satellite  is  self-luminous  to  any  sreat  eitent.  If  the 
aatellite  were  aelf-luminoua,  it  would  lie  aeen  by  Its  own  light,  and 
if  the  planet  were  luminous  the  satellite  migbt  be  see*  by  the  re- 
flected light  of  the  pUnet. 

The  motions  of  these  objects  are  connected  by  two  curious  and 
important  relations  discovered  by  La  Placb,  and  expressed  as  fol- 
lows: 

I.  Th»  mean  motim  <tf  the  flmA  mUettiU  added  to  twiee  the  mean 
motim  vf  the  tJiird  i»  mutl^  equal  to  three  timee  the  meoH  tuetim  <(f 
the  eieoiuL 

n.  ^tethe  mean  bmaitude  of  the  Jlrtt  tatettUe  m  add  twiee  the 
mean  lanfUude  <^  the  third,  ana  mUraet  three  timee  the  mean  longitude 
o/theieeond,  the  differenee  m  tdmoMe  180°. 

The  first  of  these  reUtions  is  shown  in  the  following  table  of  the 
mcian  daily  modons  of  the  satellites: 

SatelUte  I  In  one  day  moves M8°-«MW 

II       «         "  lOl'-niS 

••    III ,    60*  mw 

••     IV     "      "        2r«7n 

Motion  of  Batfvlllte  I W-m» 

Twice  tut  of  SatelUte  III 10(r-«S4 

Bam 804*  1944 

Three  times  notion  of  SatelMte  II 804°  '1944 

Observations  showed  tiiat  this  condition  was  fulfilled  as  exaetly 
as  possible,  hot  the  discovery  of  La  Plack  consisted  in  showing  tli^ 
if  the  approximate  coincidence  of  the  mean  motions  was  once  e«- 
(ablidiea,  they  could  never  deviate  itoas  exact  coincidence  with 
the  hiw.  The  cas«  is  analogous  to  that  of  the  moon,  which  alwMs 
psaanti  the  same  face  to  u«  an2  which  always  will  sinCo  the  nu- 
nott  \(Aa%  once  approziiusus'.y  t:^^  it  will  bocone  loaot  and  evo* 
lemainsOi 


850 


ABTROirOMr. 


:'>WI 


The  diwovi-  uii  the  anulu«l  prop««tioii  of  liaht  by  meMM  of 
theM  Mtellite*  h«i  ftlready  been  aeKiiMd,  and  it  rm  alM  been  ex- 
piniDed  that  they  are  of  -um  in  the  roush  determination  of  longi- 
tudea.  To  facilitate  their  obaenration,  the  Nautical  Almanac  gives 
complete  ephemerides  of  their  phenomena.  A  apecimen  of  a  por- 
timi  of  such  an  ephemeria  for  1865,  March  7th,  8th,  and  9th,  ia 
added.  The  time*  are  Washington  mean  times.  The  letter  IK  in- 
dicates that  the  phenomenon  ia  viaible  in  Waahington. 

1M0— Mahcb. 


d. 

h.    m.       $ 

I. 

Eclipse 

Diaapp 

7 

18   97    88S 

Occult. 

Bespp. 

7 

91    M 

III. 

IngTMS 

8 

7    97 

III. 

Shadow 

Bgrew 

8 

9    88 

III. 

Transit 

Ingnas 

8 

19    81 

II. 

Eellpw 

Disapp. 

8 

18      1    997 

III. 

Tranalt 

Bgnw    W. 

8 

IS     6 

II. 

Eclipse 

RMpp.    W. 

8 

18    94    111 

II. 

Oecolt. 

Diaapp   W. 

8 

18    97 

Shadow 

Ingreaa  W. 

8 

16    48 

Transit 

InRfcss  W. 

8 

18   88 

Shadow 

Egroas 

8 

17    OT 

11. 

Occult. 

Heapp 

8 

17    69 

I.' 

Transit 
Eollpss 

Um^ 

8 
9 

19    18 

19    88    88-4 

L 

Occult. 

Beapp     W. 

9 

IS   96 

Suppose  an  obsenrer  near  New  York  "City  to  have  determined  his 
local  tune  accurately,  lliis  is  about  IS"  faster  than  Waahington 
time.  On  1868,  March  8th,  he  would  look  for  the  reappearance  of 
II  at  about  18^  84"  of  bis  local  time.  Suppcw  he  obsenred  it 
at  18^  86*>  99"7  of  his  time :  then  his  meridian  is  19"  ll'-6 
east  of  WaaUngton.  The  diffleulty  of  obaerring  these  eclipses  with 
accuracy,  ai^  the  fact  that  the  aperture  of  the  teleaoope  employed 
baa  an  fanportant  effect  on  the  appearances  seen,  have  ke^  this 
nugthod  frmn  a  wide  utility,  which  it  at  first  seemed  to  promise. 

The  apparent  diameters  of  these  aatellitea  have  been  measured  by 
Sntmra,  Bboobi,  and  others,  and  the  best  results  are : 

I,  l"-0;  n,  <r-9;  in,  1"'8;  IV,  l"-8. 

Their  masses  {,J*mUer=\)  are : 

L  0*000017 ;  11,  0 000098 ;  HI,  0000088:  IV,  OHMMKMB. 

The  third  aatelUte  is  thus  the  largest,  and  it  Iws  about  the  den- 
si^  of  the  phuiet  The  true  diameters  vary  £mn  9900  to  8700 
ouiea.  ThcTolumeofn  is  about  that  of  our  moon;  III  approwdiss 
our  earth  in  size. 

Variations  in  the  light  of  these  bodies  have  constantly  been 
noticed  which  hsTc  hem  rappoeed  to  be  due  to  the  fact  that  they 
turned  on  their  axes  once  in  a  revolution,  and  thus  presented  various 
Ikoes  to  us.  The  recent  socwate  photoawtrie  ws— ntss  of  I>»ab- 
luaii  show  that  this  hypotheds  wfll  not  aooonnt  for  all  the  chwifH 
observed,  some  of  whicb  appear  to  be  quite  sudden. 


'•'piW5S!PrS?' 


r. 


{Ktion  of  light  by  mesnii  of 
M>d,  tnd  it  hH  «lio  been  e%' 
ugh  detenninttion  of  longi- 
the  Nauticftl  Almanao  givei 
leiw.  A  tpecimen  of  a  por- 
HarchTth,  8th,  and  9th,  ia 
san  times.  The  letter  TK  in- 
in  Waahiogton. 

H. 


d. 

ir 

m. 

« 

7 

18 

87 

88-8 

7 

SI 

66 

8 

7 

87 

8 

9 

68 

8 

18 

81 

8 

18 

1 

88-7 

w. 

8 

15 

6 

w. 

8 

15 

84 

111 

w. 

8 

15 

87 

w. 

8 

15 

48 

w. 

8 

16 

68 

8 

17 

m 

8 

17 

69 

8 

19 

18 

9 

18 

66 

89-4 

w. 

9 

16 

86 

City  to  haTe  detennined  hla 
18"  faater  than  Waahington 
look  for  the  reappearance  of 
M.  8uppow  he  obaenred  it 
hi*  meridian  U  18"  11-6 
Dbaerring  theae  ecUpaea  with 
e  of  the  teleacope  employed 
irancea  teen,  have  ke^  this 
t  first  seemed  to  promise, 
llites  have  been  meamred  by 
test  results  are : 
8. 

)0088:  TV.  0*000048. 
■t,  and  it  liaa  abont  the  den- 
ers  vary  from  8900  to  8700 
»f  oar  moon ;  III  approaohea 

lodies  have  ooostantly  been 
Iw  doe  to  the  fact  that  they 
n,  and  thua  presented  variooa 
mnetrle  m— sarsaof  Sksbl- 
>C  aoooont  fw  all  the  chaaf 
quUe  sudden. 


i^m^mm^^- 


BATKLLITEJH  OF  JUPITEB. 

"^      ^      P      r* 


851 


s   I   I   I 

§     §     §     § 


CHAPTER  VIII. 

SATURN  AND  ITS    SYSTEM. 


-^ 


g  1.    QEinBIlAL  DBSGBIFTIOir. 

Saturn  is  the  most  distant  of  the  major  planets  known 
to  the  ancients.  It  revolvfis  around  the  sun  in  29^  years, 
at  a  mean  distance  of  nearly  1,600,{KM},000  kilometres 
(890,000,000  miles).  The  angular  diameter  of  the  ball  of 
the  planet  is  about  Id"* 8,  corresponding  to  a  true  diam- 
eter of  about  110,000  kilometres  (70,600  miles).  Its  diam- 
eter is  therefore  nearly  nine  times  and  itc  volume  about 
700  times  that  of  the  earth.  It  is  remarkable  for  its  small 
density,  which,  so  far  as  known,  is  less  than  that  of  any 
other  heavenly  body,  and  even  less  than  that  of  water. 
Oonsequently,  itoannot  be  composed  of  rooks,  like  those 
which  form  our  earth.  It  revolves  on  its  axis,  aoeording 
to  the  recent  observations  of  Professor  Hall,  in  lO*"  14" 
24%  or  less  than  half  a  day. 

8atwm  is  perhaps  tlie  most  remarkable  planet  in  the  so- 
hur  system,  being  itself  the  centre  of  a  system  of  its  own, 
altogether  unlike  any  thing  else  In  the  heavens.  Its  most 
noteworthy  feature  is  seen  in  a  pair  of  ringi  which  sur- 
round it  at  a  considerable  distance  from  the  pbnet  itpelf. 
Outside  of  these  rings  revolve  no  iMl'tban  eight  satelBtoi, 
or  twioe  the  greatest  number  known  to  surroui^  any 
otiier  planet.  The  pknet,  rings,  and  satellitea  are  alto- 
geUier  called  the  Sahtrman  afdrnn.  lliegeDual  ^>pe■r• 
ance  of  this  system,  ae  aeen  in  a  nnall  UAmoof$t  indiown 
in  Fig.  es. 


ASPBXjr  OF  SATURN. 


363 


VIII. 

SYSTEM. 
OBIFnON. 

B  major  planets  known 
id  the  sun  in  29|  yean, 
600,()(H),000  kilometres 
r  diameter  of  the  ball  of 
onding  to  a  troe  diam- 
0,600  miles).  Itsdiaui- 
B  and  itc  volmne  abont 
remarkable  for  its  small 
is  less  than  that  of  any 
less  than  that  of  water, 
led  of  rooks,  like  those 
es  on  its  axis,  aooording 
•fessor  Hall,  in  10^  14" 

arkable  planet  in  the  so- 
of  a  system  of  its  own, 
the  heavens.  Its  mort 
or  of  rin^  which  snr- 
ifrom  thejdanet  itself. 
W^thanei^t  satellites, 
nown  to  sommiid  any 
,  and  satellites  ane  alto- 
).  Thefensnl  vpptn- 
nwll  tolMOopt,  isshown 


To  the  naked  eye,  Saturn  is  uf  a  dull  yuUoMrish  color, 
shining  with  about  the  brilliancy  of  a  star  of  Uie  iirBt  mag- 
nitude. It  varies  in  brightness,  however,  witli  the  way 
in  which  its  ring  is  seen,  being  brighter  the  wider  thb  ring 
appears.  It  comes  into  opposition  at  intervals  of  one  year 
and  from  twelve  to  fourteen  days.  The  following  are  the 
times  of  some  of  these  oppositions,  by  studying  which  one 
will  be  enabled  to  recognize  the  planet : 


Fia.  9S. 


VnW  or  TBB  BATCBIIIAH  STSfBH. 


1879 October  6th. 

1880 ;  October  IStli. 

1881 October  81st 

1889 . .  November  14th. 

1P88 MovwttberilSth. 

1884.. December  ll'h. 

During  these  yeare  it  will  be  best  seen  in  the  antnl^n 
and  winter. 


iiiMiWri  M 


I 


iit' 


i< 


ii!P 
i 


854 


ABTBONOMT. 


When  viewed  with  a  telescope,  the  pliysical  appearance 
of  the  ball  of  Satwm  is  quite  similar  to  that  of  Jitpiter, 
having  light  and  dark  belts  parallel  to  the  direction  of  its 
rotation.  But  these  cloud-like  belts  are  very  difficult  to 
see,  and  so  indistinct  that  it  is  not  easy  to  determine  the 
time  of  rotation  from  them.  This  has  been  done  by  ob- 
serving the  revolution  of  bright  or  dark  spots  which  appear 
on  the  planet  on  very  rare  occasions. 

8  2.    THB  BOrOS  OF  SATUBIT. 

The  rings  are  the  most  remarkable  and  diaracteristic 
feature  of  the  Batumian  system.  ¥1g.  96  gives  two  views 
of  the  ball  aud  rings.  The  Uf^r  cme  shows  one  of  their 
aspects  as  actually  presented  in  the  tdesoope,  and  the 
lower  one  shows  what  the  ajf^wvanoe  wouM  be  if  the 
planet  were  viewed  from  a  direetimi  at  right  anglca  to  tlie 
plane  of  the  ring  (which  it  never  cm  be  from  the  earth). 

The  first  telesoopic  observers  of  jSbrfurra  were  unable  to 
see  the  linga  in  their  true  f  onn,  and  were  greatly  per- 
plexed to  aocotrnt  for  the  appearance  which  the  planet 
presented.  Gamlho  described  the  plauetia  *'  tri-oorpo- 
rate,"  the  two  ends  of  the  ring  having,  in  his  imperfeot 
telescope,  the  appearance  of  a  pair  of  OBill  planets  at- 
tached to  the  central  one.  "  On  each  ride  of  old  Satwm 
were  servitors  who  aided  him  on  his  way."  This  sup- 
posed cUscovery  was  announced  to  his  friend  KKW.Mt  fai 
the  following  logogriph : 

smaismrmilmopoelalevmibonenogtteviTas,  which,  b^^ 
transposed,  becomes — 

"  Altiirimam  planetam  teigeminam  obsevavi"  (I  have 
ofawnrod  tho  most  distant  planet  to  be  triform)-. 

The  jdienommion  oonstantly  remiuned  a  myalery  to  ito 
lint  ohaervw.  In  1610  he  haid  seen  fhe  j^burat^MMiHiipft- 
sied,  as  he  snpposed,  by  two  lateral  stars;  in  I61i  the 
latter  had  van^hed,  and  the  central  body  alone  retnained. 
After  that  Qaulho  oeased  to  observe  Saturn. 


the  physical  appearance 
lar  to  that  of  JvpUer^ 
$1  to  the  direction  of  its 
lelts  are  very  difficult  to 
>t  easy  to  determine  the 
lis  has  been  done  by  ob- 
dark  spots  which  appear 


ns. 


F  SATUBir. 


kable  and  cluuw^ristic 
Fig.  96  gives  two  views 
r  <Hie  shows  one  of  their 
the  telescopb,  and  the 
HMranoe  would  be  if  the 
km  at  right  ang^  to  tlie 
can  be  from  the  eartli). 
)f  Sstwm  were  unable  to 
1,  and  were  greatly  per- 
inuio0  which  ^e  planet 
he  planet  as  "  tri-oorpo- 
having,  in  his  imperfect 
Niir  of  pnill  planets  at- 
1  each  side  of  old  Satmm 
m  his  way."  This  mp- 
to  his  friend  KjtFunin 

logtteviras,  which,  bring 

ninam  obsevavi"  (I  hftV9 
to  be  triform)', 
wmained  a  myaleiy  to  its 
nen  the  j^hmet^MBOOiapft- 
iterai  stsn;  in  lAU  the 
tnd  body  alone  retained. 
lervoiSbtom. 


356 


ASTBONOMY. 


:s 


/" 


Tko  appearances  of  i|ie  liDg  were  also  iacomprehensiblo 
to  Hkvklivs,  Gabsbwdi,  aud  othen.  It  was  not  until 
1655  (after  seven  yeara  of  observation)  that  the  celebrated 
HnroHKNS  discovert^  the  true  explanation  of  the  nmark- 
aUe  and  recurring  bbAvA  of  phenomena  present  by  the  tri> 
jrate  planet.  ^  , 

Le  aDnounped  his  couolusions  in  the  following  logo- 


aaaaaa  ooppo  d  eeeeegh  iiiiiii  1111  mm  nmmnonftn 
oooo  w  q  rr  s-lttti  nnnnu, "  which,  w|N»4inpp|||ed,  VM^ 
M'4miiilo  cingitar,  t«aui,  pho^  Bai||ini  ^ 
•SeqUptieam  incliii«to^' t^is|(ld|«d ^j^»|hln idtt»] 
»9iirl»rae  tooohii^j  buS^aai^  ikiii-m^^&^.  y 

Th|f>  deM^rip^  ii  eo9i|ilal<i  JMid  ^Heia^M^    \         jf^ 

In  1665  it  WIS  foonid  by  BAi^t,  of  l^iid,  liiafc^^l^ 
IltnroanB<had  tiem  «!  ,&  fi^  xing  was  >e|d3|r ii[«^    %, 
divjUon  ejEtended  allthie  %|y  tuwi^iinalui^^ 
tUs  ^vinon  is  shQ:vm  in  tij^j|garee. 

td  1860  the  MesM.  Boi^  of  Cimbridge,  fOqudjte^dlerB 
WIS  a  thirifl  ring,  of  ]|,  dtislcy-aad  ndMpiu  a<q|«w^;4pi|^ 
^  other  two,  or  ttiSbiBe  «((Mshed  t(}'||igbiiier  cl' 
kkittrring.  1ft  fs  Ihj^rafon^cnowa  as  ^ui^ 
Itliad  not  ben  befoi|l Ih&y  4e«^ba£o«l%  to|^( 
mi^-i*i  color,  whieh  made  it  adiffiofilE  |^U|p0l^to  8e|i 
ii^  a  good  teieicop0.  It  is  not  sepan|i^i(|ra  tlS  _ 
1^,  bat  seeiitt  aa  if  «MlBohed  to  it.^  ISliigfter  diiiidt«s|i|E 
tow^  its  imur  edgeV  which  morgai  pjiMlnally  into  ^ 
Avtky  ring  so  a*  to  make  it  diffisidt  ^  dedd*  pvfpiwly 
wliMV  it  ends  and  the  dosky  lAag  IwgfiDo.  T&R  Ii#|r  «x- 
toidB  aboni  (me  half  iraj  iraai  ^  inner  ec^  4;|i  Ihe 
b«%^t  ring  to  the  ball  of  the  planet. 

Aaprtt  or  the  Bioga^  As  iSnfcam  revolve  ni— nil  the 
s«^tiMpltteol  the  lings  remains  panNiltoillMlf.  timt 
ii,  tf  we  oomilwaiiw^^liiinnwiiifc  HpmjiliiJlM 
of  the  pl«iiei«fw3WiM8e«lKr.li«tlii|^||HMI..^  llttLfli^as 
the  axis  of  the  latter,  this  ttds  wffl  'idwiyif  i[mit%  the 
8unm  direction.    In  this  respeet,  the  aaotioo  is  similar  to 


IM- 


aSUMlMIMMIIM 


'wrssjRjfs^^^??'*^ 


vere  also  iucouipreheiuiblo 
vthore.  It  w«B  not  nnti] 
oration)  that  the  celebnted 
izplanation  of  Ihe  ramark- 
lomena  present  by  the  tri- 

US  in  the  following  logo- 

iiiiii  Ull  ,mni  jnmuiQimhn 
oh,  whioBli^iplged,  m$^ 

»^«ypMg>#j  .  ■">. 

ring  was  nt^y  tfOi  A. 
oolid  niaw- th»l|f|lbi^«||J9 

HMS.  -■•'■"■  ^. 

imbridge,  fbimd^^Mriiine 
d  nabnlons  aiq|^eati^>^p||l|e 
1  to'tlibibnier  ej|ffe^4^ 
imaB|^«<^^. 
■mbod^oi)^  to 
ifllo!ilij|«ipe^to8e|i 
sepantollii^in  tlii  bi^t 

' iih  laitliiter l ,.._ 

notges  pjiianallj  into  ifJie 

ffimdt  to  deeidft  jfffniiMly 

igboglns.    Thehllir^x- 

H-^e  inner  ed||»x^  the 

tnet. 

jlMn»  iwolv*^.   iiiiwinl  iTm 

mjjmmmmi0    That 


wfi!  'thfrajf  jfdKit^  tibo 
I  th^  sciotioo  is  similar  to 


RINQB  OF  SATUIiN. 


mt' 


that  of  the  earth  aroimd  the  snn.  The  ring  of  S(itum  is 
inclined  about  27°  to  the  plane  of  its  orbit.  Couhu- 
quently,  as  tlie  planet  revolves  around  the  sun,  there  is  a 
diange  in  the  direction  in  which  the  sun  shines  upon  it 
similar  to  that  which  produces  the  change  of  seasons  upon 
the  earth,  as  shown  in  Fig.  46,  page  109. 

The  corresponding  chfmges  for  Saturn  are  shown  in 
Fig.  07.    Daring  each  revelation  of  Satfuim  the  plane 


ita.  97. 


or  lATinui  AS 


BAim. 


of  the  rim(  pawea  through  Hw  son  twice.  Thia  ooenired 
in  the  yean  1863  and  1878,  at  two  opposite  points  of  the 
orUt,  ::•  aLown  in  tiie  figore.  At  two  other  points,  mid- 
way between  tlMK,  the  mm  ahinea  upon  the  plane  d!  tho^ 
ring  «fe  its  graotat  ia^nation,  about  37*".  Since  the  eartb 
iH^KHlfrMMH)  tiwa «;»  tcmUi  «8  far  from  iSb»  wmm  Stt^ 
Mm  i%  an  tOmirm  always  aefle  Saturn  tuaaify,  Jmt  wrt 
qittte,^  ii  if  he  wwe  mpon  ^mn.    Hoice  at  certain  timoi 


II 


868 


AaTBONOMT. 


the  rings  of  Satwm  are  seen  edgeway?,  while  at  other 
times  tliey  are  at  an  inclination  of  27°,  the  aspect  depend- 
ing upon  the  position  of  the  planet  in  its  orbit.  The  io\- 
lowing  are  the  times  of  some  of  the  phases  : 

1878,  Febmary  7th.—  The  edge  of  the  ring  was  turned 
toward  the  sun.  It  could  then  be  seen  only  as  a  thin 
line  of  light. 

1885. — The  planet  having  moved  forward  90°,  the  south 
side  of  the  rings  may  be  seen  at  an  inclination  of  27°. 

1891,  December. — The  planet  having  moved  90°  fur- 
iher,  the  edge  of  the  ring  is  again  turned  toward  the  sun. 

1899. — The  north  side  of  the  ring  is  inclined  toward  the 
sun,  and  is  seen  at  its  greatest  inclination. 

The  rings  are  extremely  ^ain  in  proportion  to  their  ex- 
tent. Their  form  is  mudi  the  same  as  if  they  were  cut 
out  of  large  sheets  of  thin  paper.  Consequently,  when 
their  edges  are  tamed  toward  the  earth,  they  appear  as  a 
thin  line  of  liriit,  which  can  be  seen  tmly  idtii  powerful 
tolcscopea.  With  such  telescopes,  the  pUinet  appean  as  if 
it  were  )rfwoed  through  by  a  piece  of  very  fine  wire,  the 
ends  of  which  project  on  each  aide  more  than  the  diam- 
eter of  the  pUmet.  It  has  frequently  been  ranariced  that 
tUs  appearance  is  seen  on  (me  ride  of  the  phnet,  when  no 
tnee  of  the  ring  can  be  seen  on  the  other. 

Thme  is  smnetunes  a  period  of  a  Urn  weeks  during 
whieh  the  phme  of  the  rinir»  extmdad  ontwwd,  panm  be- 
tween the  sun  and  the  earth.  That  is,  the  sun  shines  on 
one  ride  of  the  ring,  while  the  othw  or  dark  aide  is  turned 
toward  the  earth.  In  this  case,  it  seems  to  be  ratablished 
that  (Hily  the  edge  of  the  ring  is  viriUe.  If  Jiia  be  so, 
the  substance  of  the  rings  cannot  be  transparent  to  the 
sun's  rays,  else  it  woald  ba  seen  by  the  li|^t  whidi 
thh>ugh  it. 


»ii 


_ ._j  in  the  aiii|s.-lB  18S1  Otto  flmpva  era. 

MBdad  •  BolHrorthy  thaoiy  of  Aangas  fofaw  <m  in  fM  ||m||  of 
aUNim.  Pnm  all  dM  dMcriptku,  fgluM,  sad  aeasares  Mhu  by 
«w  oM«r  artfOBOMn,  it  qipeand  tlMl  two  handNd  yemagb  tlie 


^sm^:A 


RINGa  OP  SATURN. 


8ft9 


geways>,  while  at  other 
27°,  the  aspect  depend- 
t  in  its  orbit.  The  fol- 
le  phases : 

e  of  the  ring  was  turned 
be  seen  only  as  a  thin 

A  forward  90°,  the  south 
m  inclination  of  27°. 

having  moved  90°  fnr- 
1  turned  toward  the  sun. 
ng  is  inclined  toward  the 
dination. 

n  proportion  to  their  ex- 
aiae  as  if  they  were  cut 
er.  Oonsequently,  when 
le  earth,  they  appear  as  a 
seen  only  ^tii  powerfol 
L,  the  phuiet  appean  as  if 
poo  of  very  fins  wire,  the 
side  more  than  the  diam- 
lently  been  remariEed  that 
le  of  the  planet,  when  no 
theotiier. 

of  a  few  weeks  daring 
ended  ontwtud,  paasoi  be- 
rhat  is,  the  sun  shines  on 
hex  or  dark  side  is  turned 
it  seofns  to  be  4>stablished 
is  viaiMe.  If  ;his  be  so, 
tot  be  tranaparent  to  the 
by  the  light  whieli 


.—In  \m  Otto  9nmrm  pi^ 
turn  ffoiut  OB  ia  Om  mm  of 
^fBiua  memum  #vSi  by 
•t  two  liaiuiftNl  iMM  itfft  tile 


space  between  the  planet  and  the  inner  ring  was  at  least  equal  to 
tne  combined  breadth  of  the  two  rings.  At  present  this  distance 
is  less  than  one  half  of  this  breadth.  Hence  Struvk  concluded  that 
the  inner  ring  was  widening  on  the  inside,  so  that  its  edge  had  been 
approaching  the  planet  at  we  rate  of  about  l'-8  in  a  century.  The 
space  between  the  planet  and  the  inner  edge  of  the  bright  rins  is 
now  about  4',  so  that  if  Stbutb'b  theory  were  true,  the  Inner  edge 
of  the  ring  would  actually  reach  the  planet  about  the  year  8300. 
NotwithsUndiug  the  amount  of  evidence  which  Struyb  cited  in 
fayor  of  his  theory,  astronomers  generally  are  incredulous  respecting 
the  reality  of  so  extraordinary  a  change.  The  measures  necessary 
to  settle  the  question  are  so  difficult  and  the  change  is  so  slow  that 
some  time  must  elapse  before  the  theory  can  be  established,  eren  if 
it  is  true.     The  measures  of  Kaiscr  render  this  doubtful. 

Shadow  of  Planet  and  Bing.— With  any  good  telescope  it  is 
easy  to  observe  both  the  shadow  of  the  ring  upon  the  ball  of  £btor» 
and  that  of  the  ball  upon  the  ring.  The  form  which  the  shadows 
present  often  appear*  oiflerent  from  that  which  the  shadow  ought 
to  have  aooordfng  to  the  geometrical  conditions.  These  differences 
probably  wise  from  irradiation  and  other  optical  illusions. 

Oonatitutionof  tlwBingaofBafeuxn.— The  nature  of  these 
objects  has  been  a  subject  both  of  wonder  and  of  investigation  by 
mathematicians  and  astronomers  ever  since  they  were  dueovered. 
They  wore  at  first  supposed  to  be  solid  bodies ;  indeed,  from  their 
appearance  it  was  difficult  to  ooncrive  of  them  as  anything  else. 
Tne  question  then  arose :  What  keep  them  from  falling  on  the 
planet  t  It  was  shown  by  LaPlacs  tnat  a  homogeneous  and  solid 
ring  surrounding  the  punet  could  not  remain  in  a  state  of  equili- 
brium, but  must  be  preoii^tated  upon  the  central  ball  bv  the  small- 
est disturbbg  force.  HaaioinL  having  thoa|riit  that  be  saw  oer- 
tabi  irrqpilaritiai  fai  the  figure  of  tiie  ri^,  La  Flacb  ooncluded  that 
the  objwt  ooald  be  kept  in  equilibrium  by  them,  ile  simply  as- 
sumed tills,  but  did  not  attempt  to  prove  it. 

About  1850  the  fatvwtteatitm  was  agabi  begun  by  Piofeaaoca  Bean 
and  Punusa,  of  OambricGie.  The  f wmer  mppoaed  that  tlw  riQgs 
could  not  be  aolid  at  all,  baoauia  they  bad  sometimes  shown  signs  of 
being  temmrarily  broken  op  into  a  lane  mamber  of  ooneeatrie 
rings.  AtttioaghtUswaapiM)aUyaa(q^aealilhiiion.beoaiMhkM 
that  tbe  rings  must  be  liqittd.  Professor  Panum  took  «p  tin  prob- 
lem whan  La  Plaob  had  kit  it,  and  showed  that  «v«a  aaifrsgolar 
solid  riag  would  not  be  fai  eqnillbrfaim  about  Sslwm.  He  tber^DM 
adopted  the  view  of  Bomd,  that  the  rings  were  tidd ;  but  fiaitbig 
that  avan  a  fluid  riag  would  be  uastablewiaiMa  a  iMppoiVbs  M|^ 
posed  timt  aaeh  a  mppoit  aiight  be  fnniMad  by  tb*  ar' 
This  view  lias  also  been  abaadoBed, 

KisBOW 
not  form 

small  separate  pavtides,  each  of  which  wirolves  oa  Itoown 
TlMMsatelliteiianiBdivldaa^fiNrtoesBMll^baseeninaBy  tsk- 
team,  bat  so  awMiwwii  that  when  viewed  ft«m  Urn  distasna  «(  liM 
earth  timy  tipfmt  as  a  oontiauous  aaaa.  9k»fartielea  «l  4hwt  float- 


w  WW  Slav  novo  ■ombuudou. 

vm  established  beyond  reasonable  4N«bt  tbatfte  iia«  da 
a  ooBtimKNiB  mam,  but  are  real^  a  oountiMs  madtiMk  at 


! 


mm 


360  ASTSOlfOMr. 

ing  in  a  sunbeam.  This  theory  was  first  propounded  by  Cabbini, 
of  Paris,  in  1715.  It  liad  been  forgotten  for  a  century  or  more, 
wlien  it  was  rovlved  by  Professor  Ci.krk  Maxwell  in  1856.  Tliu 
latter  published  a  profound  mathematical  discussion  of  the  whole 
question,  in  which  ho  shows  that  (his  hypothesis  and  this  alone 
would  account  for  the  appearances  presented  by  the  rings. 
Kauir's  measures  of  the  dimensions  of  the  Batumian  system  are : 

BALL  or  SATinui. 

Equatorial  diameter 17''274 

Ptolar  '•       15'8tt8 

HIMOS. 

Major  axis  of  outer  ring 80"471 

'*      "     "  the  great  division lM-'«27 

••      •«     "  the  inner  edge  of  ring 27-'859 

Width  of  the  ring 5-800 

Dark  space  between  ball  and  ring 5''299 


8  8.    SATBLLTFBS  OF  SATUBH. 

Ontside  the  rings  of  Saturn  revolve  its  eight  satellites, 
the  order  and  discovery  of  which  are  shown  in  the  following 
table : 


Ka 

Nans. 

DjjUuice 

frOMl 

Ptenet. 

DiMOVsrer. 

DsteorDiwmranr. 

Mimas. 

8-8 

HerMshel. 

178»,  September  17 

EnoeladuB. 

4>8 

Hetaehel. 

1788,  Angnst  88. 

Tetbys. 

5-8 

Gkaslni. 

1084.  Maieli. 

DIone. 

6-8 

CtMdnl. 

1084.  March. 

RhML 

»-5 

QMrioi. 

1078,  DsoemberSS. 

Titan. 

M-7 

Ear" 

OMalni. 

1050.  Mareh  85. 

Hyperion. 
Japetus, 

88-8 
64-4 

1071.  Oelator. 

The  distances  from  the  planet  are  given  in  radii  of  t 
latter.     The  satellites  Mimat  and  Hyperim  are  viaibl 
only  in  the  most  powerful  teleoeopea.    The  brightest 
all  is  TVfam,  whieh  can  be  seen  in  a  tekioope  of  the  smal 
est  ordinary  riie.     Japettta  baa  the  remarkable  pecnliarK 


r. 

flrit  propounded  by  Cabsini, 
tten  for  a  century  or  more, 
IRK  Maxwkll  in  1856.  Tho 
.tical  diacussion  of  the  whole 
Is  hypothesis  and  this  alone 
sented  by  the  rings, 
of  the  Batumian  system  are : 

DRII. 

17-'274 

15-'802 

88"471 

84*'«87 

K a7-"859 

8-800 

5-'«98 


OW  BATUBH. 

'evolve  its  eight  satellites, 
1  are  shown  in  the  following 


nOVMVT* 

OalaarDIWAfwy. 

raehel. 

1780, 

September  17. 

nehel. 

1780. 

Ancutt  88. 

iririi. 

1084,  Manh. 

Hint. 

1084. 

Manh. 

■dal. 

1078, 

Deoember  88. 

ijwhens. 

1055. 

MarehSS. 

1848,  BaptMBber  10. 

■rini. 

1071, 

October. 

Bt  are  given  in  ndii  of  the 
and  Hyperitm  are  visible 
oeopes.  The  brigfateot  of 
in  a  tekooope  of  the  amall- 
the  remariable  pecnliarity 


1 


BATBLLITJIB  OF  BATUBJT. 


861 


of  appearing  nearly  as  bright  as  TiUm  when  seen  west  of 
the  planet,  and  so  faint  as  to  be  visible  only  iu  huge  tel- 
escopes when  on  the  other  side.  This  appearance  is  ex- 
plained by  supposing  that,  like  onr  moon,  it  always  pre- 
sents the  same  face  to  the  planet,  and  that  one  side  of  it  is 
black  and  the  other  side  white.  When  west  of  the  planet, 
the  bright  side  is  turned  toward  the  earth  and  the  satellite  is 
visible.  On  the  other  side  of  the  planet,  tlie  dark  side  is 
turned  toward  us,  and  it  is  nearly  invisible.  Most  of  the 
remaining  five  satellites  can  be  ordinarily  seen  with  tele- 
scopes of  moderate  power. 

The  elements  of  all  the  satellites  are  shown  in  the  fol- 
lowing table : 


BATat4jn. 

MoMwi. 

DliUMA 

fma 
SstoriL 

LoMfltade 

of 
Fwl-Sat. 

■cecn- 
tricUjr. 

Inellaa- 

Uoato 

■allptk. 

IT 

Mlnaa.... 
BneeladDs. 
Tethjra.... 

DiMW..... 

Rbaa. 

TUaa. 

HypeilMi.. 
JapetM. . . 

881 •0&8 
808-781 
180-00778 
181084880 
78-080818 
88-877088 
18-814 
4-888088 

■ 

54.80 

7018 

178-75 

814-88 

514-84 

857.10 

40-00 

851-85 

•       / 

•0080 

•185 

•0888 

•              / 

88    00 
88    00 
88    10 
88    10 
88    11 

87  84 

88  00 
18   44 

•      / 

108    00 
108    00 
107    88 
187    88 
100    84 

187  88 

188  00 
148    88 

if* 


:|  ^^.i 


u 


CHAPTER    IX. 

THE  PLANET  UKANUS. 

Uranus  wan  discovered  on  Marcli  18th,  1781,  by  Sir 
William  Hersohel  (then  an  amateur  observer)  with  a 
ten-foot  reflector  made  by  himself.  He  was  examining  a 
portion  of  the  sky  near  H  Geminorurn,  when  one  of  the 
stars  in  the  field  of  view  attracted  his  notice  by  its  pecu- 
liar appearance.  On  further  scrutiny,  it  proved  to  have  a 
planetary  diak,  and  a  motion  of  over  2*  per  hour.  Hbk- 
soHEL  at  first  supposed  it  to  be  a  comot  in  a  distant  part 
of  its  orbit,  and  under  this  impression  parabolic  orbits 
were  computed  for  it  by  various  mathematicians.  None 
of  these,  however,  satisfied  subsequent  observations, 
and  it  was  finally  announced  by  Lexell  and  La  Place 
that  the  now  body  was  a  planet  revolving  in  a  neariy 
circular  orbit.  We  can  scarcely  comprehend  now  the 
enthusiasm  with  which  this  discovery  was  received.  No 
new  body  (save  comets)  had  been  added  to  the  solar  system 
since  the  discovery  of  the  third  satellite  ciSaium  in  1684, 
and  all  the  major  planets  of  the  heavens  had  been  known 
for  thousands  of  yean. 

HsBscnxL  BUj^jested,  as  a  name  for  the  planet,  0«or- 
gium  SidtUj  and  even  after  1800  it  was  known  in  the  Eng- 
lish NatUicai  Atmanao  as  the  Georgian  Planet.  Lalakds 
suggested  Bermihd  as  its  designation,  but  this  was  judged 
too  personal,  and  finally  the  name  Uramu  was  a^ptod. 
Its  symbol  was  for  a  time  written  ^  in  raoognition  of  tiie 
name  proposed  by  Lalande. 

Uranut  revolves  about  the  sun  in  84  years.    Itsapi 
ent  diameter  as  seen  from  the  earth  yari«i  little, 


(    IX. 

[JKANU8. 

[arch  18th,  1781,  by  Sir 
mAteur  obaerver)  with  a 
f.  He  was  examining  a 
inorur/»,  when  one  of  the 
d  his  notice  by  its  pecu- 
iitiny,  it  proved  to  have  a 
over  2*  per  hoor.  Hbk- 
I  comet  in  a  distant  part 
ipression  parabolic  orbits 
B  mathematicians.  None 
lubsequent  observations, 
y  Lbxell  and  La  Plaob 
let  revolving  in  a  nearly 
9ly  comprehend  now  the 
»very  was  received.  No 
n  added  to  the  solar  system 
satellite  of  Saium  in  1684, 
heavens  had  been  known 

me  for  the  planet,  Owr- 
10  it  was  known  in  the  Eng- 
^rgian  Fhuiet.  Lalaitok 
ation,  but  this  was  judged 
uoae  Uranfue  was  adopted, 
m  ^  in  recognition  of  tlie 

on  in  84  yean.    Itsappw- 
earth  variM  little,  being 


TBS  PLANET  UttANUH. 

abont  8' '9.    Its  true  diameter  is  abont  60,0<)0  kilometres, 
and  its  fignro  is,  so  far  as  we  yet  know,  exactly  spherical. 

In  physical  appearance  it  is  a  small  greenish  disk  with- 
out markings.  It  is  possible  that  the  centre  uf  the  disk  is 
Hlightly  brighter  than  the  edges.  At  its  nearest  approach 
to  the  earth,  it  shines  as  a  star  of  the  sixtli  magnitude, 
and  is  just  visible  to  an  acute  eye  when  the  attention  is 
directed  to  its  place.  In  small  telescopes  with  low  pow- 
ers, its  appearance  is  not  markedly  different  from  that  of 
stars  of  about  its  own  brilliancy. 

It  is  customary  to  speak  of  Hebhchel's  discovery  of 
Urawus  as  an  accident ;  but  this  is  not  entirely  just,  as 
all  conditio!  I M  for  the  detection  of  such  an  object,  if  it  '>r 
isted,  were  i   '  "^Hed.     At  the  same  time  the  early  idenliti- 
cation  of  it  met  was  more  easy  than  it  would  have 

been  eleven     .j  a  earlier,  when,  as  Abaoo  points  out,  the 
planet  was  stationary. 

Sir  William  Hkrschkl  suspected  that  Urcmu*  was  ac- 
companied by  six  satellites. 

Of  the  existence  of  two  of  these  satellites  there  has 
never  been  any  doubt,  as  they  wero  steadily  observed  by 
Hbbsohkl  from  1787  until  1810,  and  by  Sir  John  Hbb- 
BOHKL  during  the  years  1828  to  1882,  as  well  as  by  other 
later  observers.  None  of  the  other  four  satellites  de- 
scribed by  Hkbsohkl  have  ever  been  seen  by  other  ob- 
serven^  and  he  was  undoubtedly  mistaken  in  supposing 
them  to  exist.  Two  additional  ones  were  discoverod  by 
Lassbll  in  1847,  and  are,  with  the  satellites  of  Mart,  the 
faintest  objects  in  tlie  sohir  system.  Neither  of  them  is 
identioal  with  any  of  the  missing  ones  of  Hebschkl.  As 
SirWiLUAM  Hbbsohbl  liad  suspected  six  satellites,  the 
following  names  for  the  true  satellites  are  generally  adopt- 
ed to  avoid  confusion : 

SAW* 

I,  Arid. Period  =    2680888 

U,  Ufkbrid. "     =    4144181 

ra,  IttflfiA»,H«BS0HBi.'8(II.). "    =    8.706897 

rV,  C»«w»,  H«BaoiWL»i  (IV.) "    =18468869 


864 


ABTRONOMr. 


U- 


:|!l 


•  ,1 


Ml. 


It  is  an  interefltinti^  question  whetTier  the  oliscrvatio 
which  Uku8ciiki.  uHHigiiud  tu  his  bupposititious  satullite 
may  not  be  eoiiipoHod  of  observations  sometimes  of  ArU 
sometimes  of  Unibrid.  In  fact,  out  of  nine  8uppos( 
observations  of  I,  one  case  alone  was  noted  by  IlEBaoHi 
iu  which  hii  positions  wore  entirely  trustwortliy,  and  < 
tliis  niglit  Umhriel  was  in  the  position  of  his  suppocM 
satollite  I. 

It  is  likely  that  vlr»«/ varies  in  bright!' •;  on  <liffere 
sides  of  the  planet,  and  the  same  phenoMi-.ion  h.u.  <il 
licen  suspected  for  Titania, 

The  moat  remarkable  feature  of  the  Mtellites  of  ViraMu  ii  th 
their  orbits  are  nearlv  perpendicular  to  the  ecliptic  instead 
haviDK  a  small  iBclination  to  that  plane,  like  those  of  all  the  orb! 
of  both  planets  and  satellites  previouKiy  known.  To  form  a  corrc 
idea  of  tne  position  of  the  ortnti,  wc  ra^st  imagine  them  tipped  ov 
until  their  north  pole  is  nearly  8°  belo  yr  the  ecliptic,  instmd  of  9 
alwve  it.  The  pole  of  the  orbit  which  should  be  considered  as  tl 
north  one  is  that  from  which,  if  an  obnervM-  look  down  upon  a  i 
Tolvins  body,  the  latter  would  seem  to  turn  in  w  direction  opposl 
that  ofthe  hands  of  4  watch.  When  the  orbit  it  tipped  over  mo 
than  a  right  angle,  the  motion  from  a  point  lu  i\v  direction  of  tl 
north  pole  of  the  ecliptic  will  seem  to  be  I  ha  n^vune  of  this  ;  itl 
therefore  sometimes  considered  to  be  rttro^adt.  This  tern  is  fi 
quently  applied  to  the  motion  of  the  utellites  of  UranM$,  but 
rather  misleading,  since  the  motion,  being  nearly  perpendicular 
the  ecliptic,  is  not  exactly  expressed  by  the  term. 

The  four  satellites  move  in  the  same  plane,  so  far  as  the  most 
fined  observatioas  have  ever  shown.  This  fact  renders  it  hig 
probable  that  the  planet  Ut(mh$  revolves  on  its  axis  in  the  sa 
plane  with  the  orbits  of  the  satellites,  and  is  therefore  aa  obi 
sphenrid  like  the  earUi.  This  conclusion  is  founded  on  the  cons 
eration  that  if  the  planes  of  the  satellites  were  not  kept  together 
some  cause,  they  would  gradually  deviate  from  each  other  owiuj 
the  attractive  force  of  the  sun  upon  the  planet.  The  difEerent  sn 
lites  would  deviate  by  different  amounts,  ud  it  would  be  eztran 
improbable  that  all  the  orbits  would  at  any  time  be  found  in 
same  plane.  Since  wo  see  them  in  the  same  plane,  we  conclude  t 
some  force  keeps  them  there,  and  the  obUteness  of  the  planet  wo 
cause  such  a  force. 


wlietlier  the  oliaervationB 
ig  tiUi)po8ititiouH  satolUte  I 
'ationH  Bometimes  of  Ariel, 
net,  out  of  nine  aupposed 
le  WHB  notod  by  IIkbsohel 
ntirely  tnwtwortliy,  and  on 

I  poaition  of  liii*  Bupposed 


in  bright )' 
jaine  pheiio 


;  on  «1  fferent 

(>  .ion  h.it.  <il8o 


the  MtelHtea  of  Uraniu  it  that 
uUr  to  the  ecliptic  initetd  of 
tlanfl,  like  thoM  of  «11  the  orbits 
jUK"y  known.  To  form  »  correct 
re  tiv  it  imagine  them  tipped  over 
jelv;  /  the  ecliptic,  instead  of  90" 
hicb  should  be  considered  as  the 
II  obaerv'M-  look  down  upon  a  re- 
m  to  turn  in  i\  direction  opposite 
hen  the  orbit  i.i  tipped  over  more 
n  a  point  iu  liv  direction  of  the 
1  to  be  Iha  r<;vcrse  of  this  ;  it  is 
be  rttrovrade.  This  tern  is  fre- 
r  the  satellites  of  Vranm,  but  is 
>n,  being  nearly  perpendicular  to 
ed  by  the  term. 

same  plane,  so  far  as  the  most  re- 
irn.  This  fact  renders  it  highly 
revolves  on  its  axis  in  the  same 
Uites,  and  is  therefore  an  obhrt« 
iclusion  is  founded  on  the  oonsld- 
tolUtea  were  not  kept  together  by 
deviate  from  each  other  owing  to 
n  the  planet.  The  different  satel- 
nounts,  and  it  would  be  eztnnely 
uld  at  any  time  be  found  in  the 
1  the  same  plane,  we  conclude  that 
the  oblateness  of  the  pkuet  would 


m 


•I 


mA 


IMAGE  EVALUATION 
TEST  TARGET  (MT-3) 


V 

J'' 


'SJ<' 


to' 


S 


; 
'  1 


1.0 


1.1 


m  IM  12.2 

Sf  U&   12.0 


IL25  lU  11.6 


t" 


Sdehces 
QirporaBan 


M^MM^^l^M^^^M 


v; 


A. 


^^•^'^ 


^ 


nWKTMMNilMn 


MMlHai 


CIHM/ICMH 


Series. 


CIHM/ICMH 
Collection  de 
microfiches. 


CwiMlian  InMltutt  for  HImofiea!  HdlcrorapniduetloiM  /  InMhut  camdlwi  d*  mlecarapreduetlom  historiquw 


'  ni'.*.."'ti!^- 


CHAPTER    X. 

THE  PLANET  NEPTUNE. 

After  the  planet  Uranus  Lad  been  observed  for  some 
thirty  years,  tables  of  its  motion  were  prepared  by 
BovvABD.  He  had  as  data  available  for  this  purpose  not 
only  the  observations  since  1781,  but  also  observations 
made  by  Le  Monnieb,  FLAjnTEKi),  an-1  others,  extending 
back  as  far  as  1695,  in  which  the  planet  was  observed  for 
a  fixed  star  and  so  recorded  in  their  books.  As  one  of 
the  chief  diffionlties  in  the  way  of  obtaining  a  theory  of 
the  planet's  motion  was  the  short  period  of  tame  during 
which  it  had  been  regnkrly  observed,  it  was  to  be  sup- 
posed that  these  ancient  observations  would  materially  aid 
in  obtaining  exact  accordance  between  the  theory  and  ob- 
servation. But  it  was  found  that,  after  allowing  for  all 
perturbations  produced  by  the  known  planets,  the  ancient 
and  modem  observations,  though  undoubtedly  referring  to 
the  same  object,  were  yet  not  to  be  reconciled  with  each 
other,  but  differed  systematically.  Bouvabd  was  forced 
to  omit  the  older  observations  in  his^  taUes,  which  were 
publudied  in  1820,  and  to  found  his  theory  upon  the 
modem  observations  alone.  By  so  doing,  he  obtained  a 
good  agreement  between  theory  and  the  observations  of 
tiie  few  yean  immediately  snooeeding  1820. 

Boo VABD  seems  to  have  formulated  the  idea  that  a  possi- 
ble canse  for  the  discrqpanoieB  noted  mig^t  be  the  exist- 
ence of  an  unknown  planet,  but  the  meagre  data  at  his 
disposal  foroed  him  to  kave  tiw  subject  nntonohed.  In 
1880  it  was  found  tliat  the  tables  wUoh  reiwesented  the 


366 


ABTRONOMT. 


motion  of  the  planet  well  in  1820-25  were  20'  in  error,  in 
1840  the  error  was  90%  and  in  1845  it  was  over  120'. 

These  progressive  and  systematic  changes  attracted  the 
attention  of  astronomers  to  the  subject  of  the  theoiy  oi 
the  motion  of  Uramis.  The  actual  discrepancy  (120')  in 
1845  was  not  a  quantity  large  in  itself.  Two  stars  of  the 
magnitude  of  Ura/nvs,  and  separated  by  only  120',  would 
be  seen  as  one  to  the  unaided  eye.  It  was  on  account  oi 
'its  systematic  and  progressive  increase  that  suspicion  was 
p excited.  Several  astronomers  attacked  the  problem  in  vari- 
ous ways.  The  elder  Stbuve,  at  Pulkova,  prosecuted  a 
search  for  a  new  planet  along  with  his  double  star  obser- 
vations ;  Bessel,  at  Koenigsberg,  set  a  student  of  his  own, 
FLEinNO,  at  a  new  comparison  of  observation  with  theo- 
ry, in  order  to  furnish  data  for  a  new  determination ; 
Akaoo,  then  Director  of  the  Observatory  at  Paris,  sug- 
gested this  subject  in  1845  as  an  interesting  field  of  re- 
search to  Le  Yerrier,  then  a  rising  mathematician 
and  astronomer.  Mr.  J.  0.  Adams,  a  student  in  Cam- 
bridge University,  England,  had  become  aware  of  the 
problems  presented  by  the  anomalies  in  the  motion  oi 
Urtmus,  and  had  attacked  this  question  as  early  as  1843. 
In  October,  1845,  Adams  communicated  to  the  Astrono- 
mer Royal  of  England  elements  of  a  new  planet  so  situated 
as  to  produce  the  perturbations  of  the  motion  of  Uraavm 
which  had  actually  been  observed.  Such  a  prediction 
SxooL  an  entirely  unknown  student,  as  Adams  then  was, 
did  not  carry  entire  conviction  with  it  A  series  of  aod 
dents  prevented  the  unknown  planet  being  looked  for  bj 
one  of  the  laifiest  telescopes  in  England,  and  so  the  mat 
ter  apparently  dropped.  It  may  be  noted,  however,  tha 
we  now  know  Adams*  elements  of  the  new  placet  to  havi 
been  so  near  the  truth  that  if  it  had  been  reidly  looked  fo 
by  the  powerful  telescope  which  afterward  ^Uscovered  it 
satellite,  it  could  scarcely  have  fiukd  of  detection. 

Bessbl's  pupil  Flbmiho  died  beforo  his  vrwk 
and   Bsbskl's  reuearohes  were  temponrily  bnra^^ 


MT. 


DISOOrSRT  OF  NBPTUNB. 


■887 


0-25  were  20*^  in  error,  in 

845  it  was  over  120". 

itic  changes  attracted  the 

subject  of  the  theoiy  of 

tual  discrepancy  (120")  in 

itself.     Two  stars  of  the 

rated  by  only  120",  would 

It  was  on  account  of 

icrease  that  suspicion  was 

acked  the  problem  in  vari- 

at  Pulkova,  prosecuted  a 

irith  his  double  star  obser- 

;,  set  a  student  of  his  own, 

of  observation  with  theo- 

or  a  new  determination  ; 

Observatory  at  Paris,  sug- 

in  interesting  field  of  re- 

1  a  rising   mathematician 

lDAMs,  a  student  in  Cam- 

lad  become  aware  of  the 

omalies  in  the  motion  of 

question  as  early  as  1848. 

imnnicated  to  the  Astrono- 

I  of  a  new  planet  so  situated 

of  the  motion  of  Urcmiut 

)rved.     Such  a  prediction 

ident,  as  Adams  then  was, 

with  it     A  series  of  aod- 

)lanet  being  looked  for  by 

England,  and  so  the  mat-^ 

\y  be  noted,  however,  that 

I  of  the  new  plavet  to  have 

had  been  leidly  looked  for 

sh  afterward  JUicoverod  its 

failed  of  detection. 

[  before  his  vrwk  was  done, 

B  temponrily  brooj^  to 


an  end.  Stbuvb'b  search  was  unsuccessful.  Only  Le 
Yebbikb  continued  his  investigations,  and  in  the  most 
thorough  manner.  He  first  computed  anew  the  pertur- 
bations of  Urtmut  produced  by  the  action  of  Jupiter  and 
Saturn.  Then  he  examined  the  nature  of  the  irregulari- 
ties observed.  These  showed  that  if  they  were  caused  by 
an  unknown  planet,  it  could  not  be  between  Saturn  and 
Urarnis,  or  else  Saturn  would  have  been  more  affected 
than  was  the  case. 

The  new  planet  was  outside  of  Uranus  if  it  existed  at 
all,  and  as  a  rough  guide  Bode'b  law  was  invoked,  which 
indicated  a  distanee  about  twice  that  of  Uranus.  In  the 
summer  of  1846,  Lb  Yebbiek  obtained  complete  elements 
of  a  new  planet,  which  would  account  for  the  oBiprved 
irregularities  in  the  motion  of  Uranus,  and  these  were 
published  in  France.  They  were  very  similar  to  those  of 
Adams,  which  had  been  communicated  to  Professor  Ohal- 
LIB,  the  Director  of  the  Observatory  of  Camlnidge. 

A  search  was  immediately  begun  by  Chalub  for  such 
an  object,  and  as  no  star-maps  were  at  hand  for  this  region 
of  the  sky,  he  began  mapping  the  surrounding  stars.  In 
so  doing  the  new  ]danet  was  actually  observed,  both  on 
August  4th  and  13th,  1846,  but  the  observati<Hu  remain- 
ing nnredueed,  and  so  the  planetary  nature  of  the  object 
was  not  reoogniied. 

In  September  of  the  sanie  year,  Le  Yekbieb  wrote  to 
Dr.  Galue,  ihen  Assistant  at  the  Observatory  of  Berlin, 
addi^  him  to  seareh  for  the  new  planet,  and  directing 
him  to  the  place  whwe  it  should  be  found.  By  the  aid 
of  an  exoelleut  star  chart  of  this  region,  which  had  just 
been  oorapleted  by  Dr.  Bbbmikbb,  tiie  planet  was'  found 
September  98d,  1846. 

The  sirict  ri^ts  of  discovery  lay  with  Lb  Ybbbibb, 
but  tiie  oommon  consent  of  mankind  has  always  credited 
Adams  with  an  equal  duure  in  the  lionor  attached  to  this 
most  brilUsat  acUevement.  Indeed,  it  was  only  by  the 
most  nnfortiuitte  soeoeisioa  of  aoddents  that  the  disoorery 


388 


ABTRONOMT. 


did  not  attach  to  Adams'  researches.  One  thing  must  j 
fairness  be  said,  and  that  is  that  the  results  of  Lk  Yei 
BiKB)  which  were  reached  after  a  most  thorough  invest 
gation  of  the  whole  ground,  were  announced  with  an  ei 
tire  confidence,  which,  perhaps,  was  lacking  in  the  oth( 
case. 

This  brilliant  discovery  created  more  enthusiasm  tha 
even  the  discovery  of  ZTroniM,  as  it  was  by  an  exerdse  < 
far  higher  qualities  that  it  was  achieved.  It  appeared  1 
savor  of  the  marvellous  that  a  mathematician  could  sa 


to  a  working  astronomer  that  by  pointing  his  telescope 
a  certain  small  area,  within  it  should  be  found  a 
major  planet.    Yet  so  it  was. 

The  general  nature  of  the  disturUng  force  which 
vealed  the  new  planet  may  be  seen  by  Fig.  98,  whi| 
shows  the  orbits  of  the  two  planets,  and  their  res[ 
motions  between  1781  and  1840.    The  inner  oirbit  is 
of  /TrofMM,  the  outer  <me  that  of  N«ptMine.    The 
passbg  from  the  former  to  the  latter  diow  the  dineti^ 
of  the  attractive  force  of  N^ptivne.    It  will  be 


mr. 

xjhes.  One  thing  mnst  in 
the  results  of  LsYeb- 
a  most  thorough  investi- 

9re  announced  with  an  en- 
was  lacking  in  the  other 

tted  more  enthuuann  than 
as  it  was  by  an  exercise  of 
achieved.    It  appeared  to 
mathematician  oonldsay 


8ATBLLITB  OF  NEPTUNB. 


369 


by  pointing  his  tekeoope  to 
it  diGold  be  fonnd  a  new 

dUtnrUng  force  wbieh  re- 
be  teen  by  Fig.  98,  which 
>lanet8,  and  their  reepective 
40.  The  inner  orbit  ia  that 
t  of  2f«ptune.  The  irowb 
le  latter  show  the  direetiona 
tiune.    It  wiU  be  wen  that 


the  two  planets  were  in  conjunction  in  the  year  1822. 
Since  that  time  Uromua  has,  by  its  more  rapid  motion, 
passed  more  than  90°  beyond  N^twne,  and  will  continue 
to  increase  its  distance  from  the  latter  until  the  begin- 
ning of  the  next  century. 

Our  knowledge  regarding  Neptv/ne  is  mostly  confined 
to  a  few  numbers  representing  the  elements  of  its  motion. 
Its  mean  distance  is  more  than  4,000,000,000  kilometres 
(2,775,000,000  miles) ;  its  periodic  time  is  164-78  yean ; 
its  apparent  diameter  is  2' '6  seconds,  corresponding  to  a 
true  diameter  of  55.000  kilometres.  Gravity  at  its  surface 
is  about  nine  tenths  of  the  corresponding  terrestrial  surface 
gravity.  Of  its  rotation  and  physical  condi^on  nothing 
is  known.  Its  color  is  a  pale  greenish  blue.  It  is  attend- 
ed by  one  satellite,  the  elements  of  whose  orbit  are  given 
herewith.  It  was  discovered  by  Mr.  Labsell,  of  Eng- 
land, in  1847.  It  is  about  as  faint  as  the  two  outer  satel- 
lites of  Urcmuty  and  requires  a  telescope  of  twelve  inches 
aperture  or  upward- to  be  well  seen. 

ELsmiiTB  or  tbb  SATBLun  or  Vmfrxma,  waou  WASHnieTOH 

Obsbrvatiohb. 


Mmo  Dtil.T  Motioa ei'-SMTQ 

P«riodieTim« 0*'870M 

Dtoton«(los.  A  =1-47814) l«'-875 

InolinaUoa  of  Orbit  to  Ediptle 145*     V 

LoDgltade  of  Node  (1860) 184'   W 

laenwwialOOTam 1*  84' 


The  gnat  Inelinatioo  of  the  orbit  ihowt  that  it  is  tamed  nearly 
epside  dowa ;  the  direetloii  of  motloii  ia  therefore  retrogade. 


CHAPTER  XI. 

THE  PHYSICAL  CONSTITUTION  OF  THE 
PLANETS. 

It  is  remarkable  that  the  eight  large  planets  of  the  Bokr 
Bystem,  conBidered  with  respect  to  their  physical  constitu- 
tion as  revealed  by  the  telescope  and  Ae  spectroscope, 
may  be  divided  into  four  pairs,  the  phuiets  of  each  pair 
having  a  great  similaiity,  and  being  quite  different  from 
the  adjoining  pair.  Among  the  most  complete  and  sys- 
tematic studies  of  the  spectra  of  all  the  planets  are  those 
made  by  Mr.  Huooins,  of  London,  and  Dr.  Voobl,  of 
Berlin.  In  what  we  have  to  say  of  the  results  of  spect/o- 
scopy,  we  shall  depend  entirely  npontho  reports  oi  these 
observers. 

Kwranry  and  Tentu. — ^Passing  outward  from  the  sun, 
the  first  pair  we  encounter  will  be  Merewry  and  Vmm. 
The  most  remarkable  feature  of  these  two  {danets  is  a  neg- 
ative rather  than  a  positive  one,  being  the  entire  absence 
of  any  certain  evidence  of  change  on  their  surfaces.  We 
have  ahvady  shown  that  Vemut  has  a  considerable  atmos- 
phere, while  there  is  no  evidence  of  any  such  atmosphere 
around  Mtircwty.  They  have  therefore  not  been  proved 
alike  in  this  respect,  yet,  on  the  other  hand,  they  have  not 
been  proved  difEerent.  In  every  other  respect  than  this, 
the  umilarity  appears  perfect.  No  permanent  markings 
have  ever  been  certainly  seen  on  the  disk  of  either.  If, 
as  is  possible,  the  atmosphere  of  both  planets  is  filled  with 
clouds  and  vapor,  no  change,  no  openings-,  and  no  for* 


purawAL  aoNsm'UTioN  of  thk  planets.   371 


I  XI. 

TUTION  OF  THE 

large  planets  of  the  solar 

0  their  physical  constitn- 
e  and  the  spectroscope, 
bhe  planets  of  each  pair 
ling  quite  different  from 
most  complete  and  sys- 
all  the  planets  are  those 
don,  and  Dr.  Yooel,  of 
of  the  results  of  spect/o- 

apon  the  reports  ot  these 

Df  outward  from  the  sun, 
be  Mercwry  and  Venua. 
these  two  {danets  is  a  neg- 
beingthe  entire  absence 
«  on  their  surfaces.  We 
has  a  considerable  stmos- 
B  of  any  such  atmosphere 
Mieforenot  been  proved 
)ther  hand,  they  have  not 
y  other  respect  than  this, 
No  permanent  markings 

1  the  disk  of  either.  If, 
both  planets  Is  filled  with 
no  openingsj  and  no  forr 


mations  among  these  cloud  masses  are  visible  from  the 
earth.  Whenever  either  of  these  planets  is  in  a  certain 
position  relative  to  the  earth  and  the  sun,  it  seemingly 
presents  the  same  appearance,  and  not  the  slightest 
change  occurs  in  that  appearance  from  the  rotation  of  the 
planet  on  its  axis,  which  every  analogy  of  the  solar  sys- 
tem leads  us  to  believe  must  take  place. 

When  studied  with  the  spectroscope,  the  spectra  of 
Mercury  and  Ventu  do  not  differ  strikingly  from  that  of 
the  sun.  This  would  seem  to  indicate  that  the*  atmos- 
pheres of  these  planets  do  not  exert  any  decided  absorption 
upon  the  rays  of  light  which  pass  through  them  ;  or,  at 
least,  they  absorb  only  the  samo  rays  which  are  absorbed 
by  the  atmosphere  of  the  sun  and  by  that  of  the  earth. 
The  one  point  of  difference  which  Dr.  Yooel  brings  out 
is,  that  the  lines  of  the  spectrum  produced  by  the  absorp- 
tion of  our  own  atmosphere  appear  darker  in  the  spectrum 
of  Venus.  If  this  were  so,  it  would  indicate  that  the  at- 
mosphere of  Venut  is  similar  in  constitution  to  that  of 
our  earth,  because  it  absorbs  the  same  rays.  But  the 
means  of  measuring  the  darkness  of  the  lines  are  as  yet 
so  imperfect  that  it  is  impossible  to  speak  with  certainty 
on  a  point  like  this.  Dr.  Yookl  thinks  that  the  light 
from  Vmu9  is  for  the  most  part  reflected  from  clouds  in 
the  higher  region  of  the  planet's  atmosphere,  and  thertf- 
lore  reaches  ub  without  passing  through  a  great  depth  of 
that  atmosphere. 

Tb»  awfh  and  Kin.— These  planets  are  distinguished 
from  all  the  others  in  that  their  viable  surfaces  are  marked 
by  permanent  features,'  which  show  them  to  be  mJ&d,  and 
which  can  be  seen  from  thi-  other  heavenly  bodies.  It  is 
trae  that  we  cannot  stud.  i>  e  earth  from  any  other  body, 
but  we  can  foaa  a  very  oov.  dot  idea  how  it  woold  look  if 
seen  in  this  way  (from  the  moon,  for  instance).  Wherever 
the  atmoq>here  was  dear,  the  outlines  of  the  continents 
and  oceans  would  be  visible,  while  they  would  be  inviiiUe 
where  the  air  was  doa^y. 


vn 


A8TR0N0MT. 


Now,  BO  far  as  we  can  judge  from  obeervfttions  made 
at  10  great  a  distance,  never  much  lees  than  forty  mil- 
lions of  miles,  the  planet  MaT$  presents  to  our  tele- 
scopes  very  much  the  same  general  i^ypearaiioe  tiiat  the 
earth  would  if  observed  from  an  equally  great  distance. 
The  only  exception  is  that  the  visible  surface  of  Mtw§  is 
seemingly  much  less  obscured  by  clouds  than  that  of  the 
earth  would  be.  In  other  words,  that  planet  has  a  more 
sunny  sky  than  ours.  It  is,  of  course,  impossible  to  say 
what  conditions  we  might  find  could  we  take  a  much 
closer  view  of  Mara :  all  we  can  assert  is,  that  so  far  as 
we  can  judge  from  this  distance,  its  surface  is  like  that  of 
the  earth. 

This  supposed  similarity  is  strengthened  by  the  spectro- 
scopic observations.  The  lines  of  the  spectrum  due  to 
aqueous  vapor  in  our  atmosphere  are  found  by  Dr.  Yookl 
to  be  so  much  stronger  in  Mara  as  to  indicate  an  absorp- 
tion by  such  vapor  in  its  atmosphere.  Dr.  HirooiHs  had 
previously  made  a  more  decisive  observation,  having 
found  a  well-marked  line  to  which  there  is  no  omrespond- 
ing  strong  line  in  the  solar  spectrum.  Thii  would  indi- 
cate that  the  atmosphere  of  Mwa  contains  some  element 
not  found  in  our  own,  but  the  observations  are  too  diffi- 
cult to  allow  of  any  well-established  theory  being  yet 
built  upon  them. 

Jupiter  and  Batum. — The  next  pair  of   planets    arel 
Jupiter  and  Sdtwm.    Their  peculiarity  is  that  no  solid] 
crust  or  surface  is  visible  from  without.    In  this 
they  differ  from  the  earth  and  Jfar«,  and  resemble  M«r\ 
ewry  and   Vetvua.    But  they  differ  from  the  latter  in  tl 
very  important  point  that  constant  changes  can  be  seeij 
going  on  at  their  surfaces.       The  nature  of  these 
has  been  discussed  so  fully  in  treating  of  these  planets  in] 
dividnally,  that  we  need  not  go  into  it  more  fully  at  pr 
ent.    It  is  sufficient  to  say  that  the  preponderance  of  e^ 
dence  is  in  favor  of  the  view  that  ^ese  planets  have  n{ 
■olid  crusts  whatever,  but  consist  of  masses  of  molt 


r. 

from  obeervfttions  made 
ich  less  than  forty  mil- 
presents  to  oar  tele- 
mi  appearanoe  tint  tbe 
equally  great  distance, 
lible  surface  of  Uw  is 
doads  than  that  of  the 
that  pUmethas  a  more 
course,  impossible  to  say 
could  we  take  a  much 
assert  is,  that  so  far  as 
its  surface  is  like  that  of 

sngthened  by  the  speotro- 
of  the  spectrum  due  to 
)  are  found  by  Dr.  Yoou 
as  to  indicate  an  absorp- 
pbere.  Dr.  Hooonra  bad 
j}ive  obeerration,  having 
ch  there  is  no  omrespond- 
^trum.  This  would  indi- 
(r«  contains  some  dnnent 
observations  an  toodiffl- 
iblished  theory  being  yet 

lext  pair  of  planets  are 
eculiarityis  that  no  solid 
1  without.  In  this  respect 
Jtfar«,  and  resemble  Mer- 
liffer  from  the  latter  in  the 
Btant  changes  can  be  seen 
'he  nature  of  these  changes 
reating  of  these  planets  in- 
» into  it  more  fully  at  pres- 
;  the  preponderance  of  evi- 
that  tiiese  planets  have  no 
nsist  of  masses  <tf  molten 


PHYBKAL  OOirsriTUTIOy  OF  THtB  PLANBTS.    878 

matter,  surrounded  by  envelopes  of  vapor  constantly  rising 
from  the  interior. 

The  view  that  the  greater  part  of  the  apparent  voliune  of 
these  planets  is  made  of  a  seethiug  maeti  of  vapor  is  further 
strengthened  by  their  very  small  specific  gravity.  This 
can  be  accounted  for  by  supposing  that  the  liquid  interior 
is  nothing  more  than  a  comparatively  small  central  core, 
and  that  the  greater  part  of  the  bulk  of  each  planet  is 
composed  of  vapor  of  small  density. 

That  the  visible  surfaces  of  Jupiter  and  ScUvm  are  cov- 
ered by  some  kind  of  an  atmosphere  follows  not  only  from 
the  motion  of  the  cloud  forms  seen  there,  but  from  the 
spectroscopic  observations  of  Huooinb  in  1864.  He 
found  visible  absorption-bands  near  the  red  end  of  the 
spectrum  of  each  of  these  planets.  Vooel  found  a  com- 
plete similarity  between  the  spectra  of  the  two  planets, 
the  most  marked  feature  being  a  dark  band  in  Uie  red. 
What  is  worthy  of  remark,  though  not  at  all  surprising,  is 
that  this  band  is  not  found  in  the  spectrum  of  8atwm^$ 
rings.  This  is  what  we  should  expect,  as  it  is  hardly  pos- 
sible that  these  rings  should  have  any  atmosphere,  owing 
to  their  very  small  mass.  An  atmosphere  on  bodies  of  so 
slight  an  attractive  power  would  expand  away  by  its  own 
elasticity  and  be  all  attracted  around  the  planet. 

Vrairaa  and  Neptune.— Those  planets  have  a  strikinj^y 
similar  aspect  when  seen  through  a  telescope.  They 
differ  from  JvpUer  and  Salwm  in  that  no  changes  or  va- 
riations of  color  or  aspect  can  be  made  out  upon  their  sur- 
hoea ;  and  from  the  earth  and  Mara  in  the  absence  of  any 
permanent  features.  Telescopically,  therefore,  we  might 
classify  them  with  Merowry  and  Ven/ut^  but  the  spectro- 
scope reveals  a  constitution  entirely  different  from  that  of 
any  other  planets.  The  most  marked  features  of  their 
spectra  are  very  dark  bands,  evidently  produced  by  the 
absorption  of  dense  atmospheres.  Owing  to  the  extreme 
faintnees  of  the  Ught  whidi  reaohee  us  from  these  distant 
bodies,  the  regular  lines  of  the  sohr  spectrum  are  entirely 


874 


ASTRONOMT. 


td 


-  -Q 


—  H 


invisible  in  their  speotra,  yot  these  dark  bandu  which  are 
peooliar  to  them  have  been  seen  by  Uuuuinb,  Bkuuhi, 

VuoKL,  and  perhaps  others. 

Tliis  classitication  of  the 
eight  planets  into  pairs  is  ren- 
dered yot  more  striking  i>y 
the  fact  that  it  applies  to 
what  we  have  been  able  to 
discover  respecting  the  rota- 
tions of  these  bodies.  The 
S  rotation  of  the  inner  pair, 
Mercury  and  Venna,  has 
eluded  detection,  notwith- 
itanding  their  comparative 
proximity  to  us.     The  next 

pair,  the  earth  and  Mar$y 
have  perfectly  definite  times 
of  rotation,  because  their 
outer  surfaces  consist  of  solid 
crusts,  every  part  of  which 
must  rotate  in  the  same  time. 
The  next  pair,  Jupiter  and 
Saturn,  have  well-established 
times  of  rotation,  but  these 

G  times  are  not  perfectly  defi- 

nite, because  the  surfaces  of 
I  these  pUnets  are  not  solid, 
I  and  different  portions  of  their 
^  I  mass  may  rotate  in  slightly 
■■■■■■■■■Ji  different  times.  JwpUer  and 
Fie.  W.— apioTBuit  o»  cbamub.  gatium  have  also  in  common 
a  very  rapid  rate  of  rotation.  Finally,  the  outer  pair,  Ura- 
nu»  and  Neptnme,  seem  to  be  surrounded  by  atmosphere^  of 
such  density  that  no  evidence  of  rotation  can  be  gathered. 
Thus  it  seems  that  of  the  eight  phmets,  only  the  central 
fonr  have  yet  Certainly  indicated  a  rotation  on  their  axet. 


dark  band*  which  are 
by  UuooiNB,  Bkcchi, 
,  and  perhaps  othorB. 
,   classitlcation   of    the 
ilanete  into  pairs  is  ron- 
yct  more  etriking  by 
ict    that  it  applies  to 
we  have  been  able  to 
er  respecting  the  rota- 
of  these  bodies.     The 
tn  of    the  inner  pair, 
try    and     Ventu,    has 
I    detection,     notwith- 
ng    their   comparative 
nity  to  us.     The  next 
the  earth  and    Mara, 
perfectly  definite  times 
otation,    because    their 
surfaces  consist  of  solid 


J,  every  part  of 


which 
rotate  in  the  same  time, 
next  pwr,  Jupiter  and 
ni,  have  well-established 
i  of  rotation,  but  these 
»  are  not  perfectly  defl- 
because  the  surfaoes  of 
)  planets  are  not  solid, 
lifferent  portions  of  their 
I  may  rotate  in  slightly 
rent  times.     Jupiter  and 
tm  have  also  in  common 
ally,  the  outer  pair.  Urn- 
■onnded  by  atmospherepol 
rotation  can  be  gathered. 
it  planets,  only  the  central 
la  rotation  on  their  azw. 


CHAPTER    XII. 

METEORS. 

%  1.    FHBVOMBNA  AND  OAUBBB  OT  lOVnOBS. 

Dunmo  the  present  century,  evidence  has  been  collected 
that  countless  masses  of  matter,  far  too  small  to  be  seen 
with  the  most  powerful  telescopes,  are  moving  througli 
the  planetary  spaces.  This  evidence  is  afforded  by  the 
phenomena  of  *< aerolites,"  << meteors,"  and  "shooting 
stars."  Although  these  several  phenomena  have  been  ob- 
served and  noted  from  time  to  time  sinc^  the  earliest  his- 
toric era,  it  in  only  recently  that  a  'complete  explanation 
has  been  reached. 

AeroUtM. — ^Reports  of  the  falling  of  laif;e  masses  of 
stone  or  iron  to  the  earth  have  been  familiar  to  antiqua- 
rian students  for  many  centuries.  Araoo  has  collected 
several  hundred  of  these  reports.  In  one  instance  a  monk 
was  killed  by  the  fall  of  one  of  these  bodies.  One  or  two 
other  cases  of  death  from  this  cause  are  supposed  to  have 
occurred.  Notwithstanding  the  number  of  instances  on 
record,  aerolites  fall  at  such  ^vide  intervals  as  to  be  ob- 
served by  very  few  people,  consequently  doubt  was  fre- 
quently cast  upon  the  correctness  of  the  narratives.  The 
problem  where  such  a  body  could  come  from,  or  how  it 
could  get  into  the  atmosphere  to  fall  down  again,  f ormorly 
seemed  so  nearly  incapable  of  solution  that  it  required 
some  orednlity  to  admit  the  facts.  When  the  evidence 
became  so  strong  as  to  be  indiq>ntable,  theories  of  their 
origin  began  to  be  impounded.    One  theory  quite  fashion- 


^. 


^.^^  »- 


Aj^t'^^^'^^ 


376 


A8TR0N0MT. 


able  in  the  early  part  of  this  century  was  that  they  were 
thrown  from  volcanoes  in  the  moon.  This  theory, 
though  the  subject  of  mathematical  investigation  by  La 
Place  and  others,  is  now  no  longer  thought  of. 

The  proof  that  aerolites  did  really  fall  to  the  ground 
first  became  conclusive  by  the  fall  being  connected  with 
other  more  familiar  phenomena.  Nearly  every  one  who 
is  at  all  observant  of  the  heavens  is  familiar  with  holiies, 
or  lire-ballB — ^brilliant  objects  having  the  appearance  of 
rockets,  which  are  occasionally  seen  moving  with  great  ve- 
locity through  the  upper  regions  of  the  atmosphere. 
Scarcely  a  year  passes  in  which  such  a  body  of  extraordi- 
nary brilliancy  is  not  seen.  Generally  these  bodies,  bright 
though  they  may  be,  vanish  without  leaving  any  trace,  or 
making  themselves  evident  to  any  sense  but  that  of  sight. 
But  on  rare  occasions  their  appearance  is  followed  at  an 
interval  of  several  minutes  by  loud  explosions  like  the  dis- 
charge of  a  battery  of  artillery.  On  still  rarer  occasions, 
masses  of  matter  fall  to  the  ground.  It  is  now-  fully 
understood  that  the  fall  of  these  aerolites  is  always  ac- 
companied by  light  and  sound,  though  the  light  may  be 
invisible  in  the  daytime. 

When  chemical  analysis  was  applied  to  aerolites,  they 
were  proved  to  be  of  extramundane  origin,  because  they 
contained  chemical  combinations  not  found  in  terrestrial 
substances.  It  is  true  that  they  contained  no  new  chemi- 
cal elements,  but  only  combination  of  the  elements  which 
are  found  on  the  earth.  These  combinations  are  now  iM> 
familiar  to  mineralogists  that  they  can  distinguish  an 
aerolite  from  a  minend  of  terrestrial  origin  by  a  careful 
examination.  One  of  the  largest  components  of  these  | 
bodies  is  iron.  Specimens  having  very  much  the  appear- 
ance of  great  masses  of  iron  are  found  in  the  National  | 
Museum  at  Washington. 

MMeon. — Although  the  meteors  we  hare  described  are] 
ofdaBEling  briUiancy,  yet  they  run  byinsenriMe  gtftda-l 
tians  into  j^eaomeaa,  whioh  any  ono  oan  see  on  ttiy  etawl 


>  iiiiri.M 


CAUSE  OF  METBORa. 


377 


iry  was  that  they  were 
moon.     This    theory, 
sal  investigation  by  La 
ir  thought  of. 
lally  fall  to  the  ground 
being  connected  with 
Nearly  every  one  who 
is  familiar  with  Joif ^, 
ring  the  appearance  of 
n  moving  with  great  ve- 
os  of   the   atmosphere, 
ch  a  body  of  extraordi- 
irally  these  bodies,  bright 
>nt  leaving  any  trace,  or 
'  sense  but  that  of  sight, 
irance  is  followed  at  an 
d  explosions  like  the  dis- 
On  still  rarer  occasions, 
ound.     It   is  now  fully 
e  aerolites  is  always  ac- 
hough  the  light  may  be 

applied  to  aerolites,  th^ 
lane  origin,  because  they 
)  not  f  oimd  in  terrestrial 
contained  no  new  chemi- 
on  of  the  elements  which 
combinations  are  now  so 
they  can  distinguish  an 
Btrial  origin  by  a  careful 
lest  ooroponents  of  these 
og  very  much  the  appear- 
re  found  in  the  National 

3on  we  hare  described  are 
^  run  by  intenrible  gnd** 
J  ODO  on  M6  on  tay  etetf 


night.  Tlie  most  brilliant  meteors  of  all  are  likely  to  be 
seen  by  one  person  only  two  or  three  times  in  his  life. 
Meteors  having  t!ie  appearance  and  brightness  of  a  distant 
rocket  may  be  seen  several  times  a  year  by  any  one  in  the 
habit  of  walking  out  during  the  evening  and  watching  the 
ricy.  Smaller  ones  occur  more  frequently  ;  and  if  a  care- 
f nl  watch  be  kept,  it  will  be  found  that  several  of  Ihe 
faintest  class  of  all,  familiarly  known  as  shooHnff  ttara^  can 
be  seen  on  every  clear  night.  We  can  draw  no  distinction 
between  the  most  brilliant  meteor  illuminating  the  whole 
sky,  and  perhaps  making  a  noise  like  tlmnder,  and  the 
faintest  shooting  star,  except  one  of  degree.  There  seems 
to  be  every  gradation  between  these  extremes,  so  that  all 
should  be  traced  to  some  common  cause. 

Oanae  of  Meteor*. — There  is  now  no  doubt  that  aU  thees 
phenomena  have  a  common  origin,  being  due  to  the  earth 
encountering  innumerable  small  bodies  in  its  annual  course 
around  the  sun.  The  great  difficulty  in  connecting  mete- 
ors with  these  invisible  bodies  arises  from  the  brilliancy 
and  rapid  disappearance  of  the  meteors.  The  question 
may  be  asked  why  do  they  bum  with  so  great  an  evolu- 
tion of  light  on  reaching  our  atmosphere  ?  To  answer  this 
question,  we  must  have  recourse  to  the  mechanical  theory 
of  heat  It  is  now  known  that  heat  is  really  a  vibratory 
motion  in  the  particles  of  solid  bodies  and  a  progressive 
motion  in  those  of  gases.  By  making  this  motion  more 
impid,  we  make  the  body  warmor.  By  simply  blowing  air 
•l^niifc  any  combustible  body  with  sufficient  velocity,  it 
can  be  set  on  fire,  and,  if  incombustible,  the  body  wUl  be 
made  red-hot  and  finally  melted.  Experimmts  to  deter- 
mine the  degree  of  temperature  thus  produced  have  been 
made  by  Sir  Wiluax  Thokpson,  who  finds  that  a  veloci- 
ty of  about  60  metres  per  second  corresponds  to  a  rise  of 
temperatnie  of  <me  degree  Oentigrade.  From  this  the 
temperature  due  to  any  velodty  can  be  readily  calculated 
on  tile  prineiple  that  tiie  increase  of  temperature  is  pro- 
portiooel  to  the  "  enogy"  of  tiie  particles,  which  agsin 


378 


ASTRONOMY. 


is  proportional  to  the  square  of  the  velocity.  Hence  a 
veloci^  of  500  metres  per  second  would  correspond  to  a 
rise  of  100"  above  the  actual  temperature  of  the  air,  so 
that  if  the  latter  was  at  the  freezing-point  the  body  would 
be  raised  to  the  temperature  of  boiling  water.  A  velocity 
of  1500  metres  per  second  would  produce  a  red  heat.  This 
velocity  is,  however,  much  higher  than  any  that  we  can 
produce  artificially. 

The  earth  moves  ..round  the  sun  with  a  velocity  of 
about  30,000  metres  per  second  ;  consequently  if  it  met  a 
body  at  rest  the  concussion  between  the  latter  and  the  at- 
mosphere would  correspond  to  a  temperature  of  more  than 
800,000°.  This  would  instantly  dissolve  any  known  sub- 
stance. 

As  the  theory  of  this  dissipation  of  a  body  by  moving 
with  planetary  velocity  through  the  upper  regions  of  our 
air  is  frequently  misunderstood,  it  is  necessary  to  explain 
two  or  three  points  in  connection  with  it. 

(1.)  It  must  be  remembered  that  when  we  speak  of 
these  enonnouB  temperatures,  we  are  to  consider  them  as 
potential,  not  actual,  temperatures.  We  do  not  mean 
that  the  body  is  actually  raised  to  a  temperature  of  800,- 
000°,  but  only  that  the  air  acts  upon  it  as  if  it  were  put 
into  a  furnace  heated  to  this  temperature — ^that  is,  it  is 
rapidly  destroyed  by  the  intensity  of  the  heat. 

(2.)  This  potential  temperature  is  independent  of  the 
density  of  the  medium,  bdng  the  same  io  the  rarest  as  in 
the  densest  atmosphere.  But  the  actual  effect  on  the 
body  is  not  so  great  in  a  rare  as  in  a  dense  atmosphere. 
Every  one  knows  that  he  can  hold  his  hand  for  some  time 
in  air  at  the  temperature  of  boiling  water.  The  nurerthe 
air  the  higher  the  temperature  the  hand  would  bear  without 
injury.  In  an  atmosphere  as  rare  as  ours  at  ihe  height  of 
50  miles,  it  is  probable  that  the  hand  could  be  held  for  an 
indefinite  period,  though  its  temperature  dionld  betfuit 
of  ied>hot  iron  ;  henoe  the  meteor  is  not  consumed  so  rap- 
idly as  if  it  struck  a  dense  atmosphere  with  planetaiy 


irtWIIIMi.tl 


CAUSE  OF  MSTEORS. 


879 


Hence  a 
eepond  to  a 

the  air,  so 
body  would 

A  velocity 
Iheat.  This 
that  we  can 

velocity  of 
^  if  it  met  a 
■  and  the  at- 
)f  more  than 

known  snb- 

y  by  moving 
igions  of  onr 
y  to  explain 

we  speak  of 
ider  them  as 
lo  not  mean 
ore  of  300,- 
it  were  put 
-that  is,  it  is 

ident  of  the 
lo  rarest  as  Ui 
effect  on  the 
atmosphere, 
or  some  time 
The  rarer  the 
1  bear  without 
die  hei|^t  of 
»e  held  for  an 
lonld  betiiat 
nunedsorap- 
iih  planetaiy 


velocity.  In  the  latter  case  it  would  probably  disappear 
like  a  flash  of  lightning. 

(8.)  The  amount  of  heat  evolved  is  measured  not  by  that 
which  would  result  from  the  combustion  of  the  body,  but 
by  the  vU  viva  (energy  of  motion)  which  the  body  loses  in 
the  atmosphere.  The  student  of  physics  knows  that  mo- 
tion, when  hist,  is  changed  into  a  definite  amount  of 
heat.  If  we  calculate  the  amount  of  heat  which  is  equiv- 
alent to  the  energy  of  motion  of  a  pebble  having  a  veloc- 
ity of  20  miles  a  second,  we  shall  find  it  sufficient  to  raise 
about  1300  times  the  pebble's  weight  of  water  from  the 
freezing  to  the  boiling  point.  This  is  many  times  as  much 
heat  as  could  result  from  burning  even  the  most  combusti- 
ble body. 

(4.)  The  detonation  which  sometimes  accompanies  the 
passage  of  very  brilliant  meteors  is  not  caused  by  an  ex- 
plosion of  the  mef«or,  but  by  the  concussion  produced  by 
its  rapid  motion  throogh  the  atmosphere.  This  concos- 
sion  is  of  much  the  same  nature  as  that  produced  by  a 
flash  of  lightning.  The  air  is  suddenly  condensed  in  ^nt 
of  the  meteor,  while  a  vacuum  is  left  behind  it. 

The  invisible  bodies  which  produce  meteors  in  the  way 
just  described  have  been  called  meteoroidt.  Meteoric 
phenomena  depend  very  largely  upon  the  nature  of  the 
meteoroids,  and  the  direction  and  velocity  with  whidi 
they  are  moving  relatively  to  the  eartii.  With  very  rare 
exceptions,  they  are  so  small  and  fusible  as  to  be  eutirely 
dissipated  in  the  upper  regions  of  the  atmosphere.  Even 
of  those  so  hard  and  solid  as  to  produce  a  brilliant  li^^t 
and  the  loudest  detonation,  only  a  small  proportion  reach 
the  earth.  It  has  sometimes  happened  that  the  meteoroid 
only  graces  the  atmosphere,  passing  horiaontally'throiigh 
its  higher  strata  for  a  great  distanoe  and  oontinuing  its 
com  ;  after  leaving  it.  On  rare  occasions  the  body  is  so 
hard  and  nuiisive  as  to  reach  the  earth  without  being  en< 
t^rely  oomnuned.  The  potential  heat  produced  by  ito 
paannge  through  the  atmoaph^v  is  then  all  expended  in 


880 


A8TR0N0MT. 


i  ' 


melting  and  destroying  its  outer  layers,  the  inner  nnclens 
remaining  unchanged.  When  such  a  body  first  strikes 
tlie  denser  portion  of  the  atmosphere,  the  resistance  be- 
comes so  great  that  the  body  is  generally  broken  to  pieces. 
Hence  we  very  often  find  not  simply  a  single  aerolite, 
but  a  small  shower  of  them. 

Heights  of  Keteon. — ^Many  observations  have  been 
made  to  determine  the  height  at  which  meteors  are  seen. 
This  is  effected  by  two  observers  stationing  themselves 
several  miles  apart  and  mapping  out  the  courses  of  such 
meteors  as  they  can  observe.  In  order  to  be  sure  that  the 
same  meteor  is  seen  from  both  stations,  the  time  of  each 
observation  must  be  noted.  In  the  case  of  very  brilliant 
meteors,  the  path  is  often  determined  with  considerable 
precision  by  the  direction  in  which  it  is  seen  by  accidental 
observers  in  various  regions  of  the  country  over  which  it 


The  general  result  from  numerous  observations  and  in- 
vestigations of  this  kind  is  that  the  meteors  and  diooting 
stars  commonly  commence  to  be  visible  at  a  height  of 
about  160  kilometres,  or  100  statute  miles.  The  separate 
roeults  of  course  vary  widely,  but  this  is  a  rough  mean  of 
them.  They  are  generally  dissipated  at  about  half  this 
height,  and  therefore  above  the  highest  atmosphere  which 
reflects  the  rays  of  the  sun.  From  this  it  may  be  inferred 
that  the  earth's  atmosphere  rises  to  a  hei^t  of  at  least 
J  80  kilometres.  This  is  a  much  greater  he^ht  than  it  was 
formerly  supposed  to  have. 


S  a.  lornoBio  showmbs, 

As  already  stated,  the  phenomena  of  shooting  ttan  may 
be  seen  by  a  careful  observer  on  almost  any  clear  night. 
In  general,  not  more  than  three  or  four  of  them  will  be 
seen  in  an  hour,  and  these  will  be  so  minute  as  hwdly  to 
attract  uotioe.  But  they  sometimes  fidl  in  sneh  numbers 
as  to  present  the  appeanmee  of  a  meteoric  shower.    On 


y.mmU!ii:iissssa 


^4i?iMu:»AkB  t*-  .ui>«. 


inner  nnclens 
y  first  strikes 

resistance  be- 
oken  to  pieces, 
single  aerolite, 

ns  have  been 
teors  are  seen, 
ing  themselves 
lonrses  of  such 
Ki  sore  that  the 
e  time  of  each 
f  very  brilliant 
th  considerable 
in  by  accidental 
f  over  which  it 

vations  and  in- 
"B  and  shooting 
at  a  height  of 
The  separate 
I  rongfa  mean  of 
abonthalf  this 
noephere  which 
may  be  inferred 
ifl^t  of  at  least 
ight  than  it  < 


loting  Stan  may 
ny  clear  night. 
>f  them  wUl  be 
te  as  hwrdlyto 
ifoeh  nnmben 
0  abower.    On 


-wmmmmmsF 


METSOniO  8H0WER8. 


881 


rare  occasions  the  shower  has  been  so  striking  as  to  fill  the 
beholders  with  terror,  liie  ancient  and  mediieval  records 
contain  many  accounts  of  these  phenomena  which  have 
been  brought  to  light  through  the  researches  of  antiqua- 
rians. The  following  is  quoted  by  Professor  I^swton 
from  an  Arabic  record  : 

"  In  the  year  699,  on  the  lait  day  of  Mohairem,  ttan  shot  hither 
and  thither,  and  flew  againat  each  other  liJke  a  swariB  of  locnite ; 
this  phenomena  huted  until  dayhruak ;  people  were  thrown  into 
consternation,  and  made  eappHfiation  to  toe  Soet  High  :  there  was 
never  the  like  eeen  except  on  tiie  ccnning  of  tiie  mcsienger  of  Ood, 
on  whom  be  be&edietion  and  peaee."  ' 

It  hn  long  been  known  that  some  ahowen  of  this  da« 
oocnr  at  an  interval  of  about  a  third  of  a  oeutniy.  One 
was  obaeiyed  by  Humbolot,  on  the  Andes,  tm  tl»  night 
of  November  12th,  1799,  hating  from  two  o'ekxok  i^ 
daylight.  A  great  shower  was  seen  in  this  oopntiyin 
1688,  and  is  well  known  to  have  stmck  the  negroes  of  the 
SontlMm  States  with  terror.  The  theory  that  tlw  dioir*' 
era  cNMur  at  intervals  of  84  years  was  now  propfrandefi  hgr 
OuNEM,  who  predicted  a  return  of  the  shower  in  IMf  i 
This  prodietion  was  omnpletely  fulfilled,  but  histewl  ol  mg^ 
peering  in  the  year  1867  only,  it  was  first  notioed  in  18M, 
On  the  n^ht  of  November  18th  of  that  year  »  reaDiribMe 
shower  was  seen  hi  Enrope,  while  on  tiie  oeneipentipf 
night  of  iiie  year  following  it  was  agifki  seen  te  tils  emuir 
try,  and»  ftilMt,  was  rapei^  fortwo  or  three  yieni,  gmi* 
ndly  dj^ng  eway. 

The  ooenneBee  of  e  drawer  ol  meteom  evideaftly  duypi^^ 
tii*^  eertii  eneoanteni  e  swwm  of  meteoroNk  Thm 
leeidienoe  «t  the  same  thne  of  the  ye«r,  when  iSb»  ewtib 
ieilliMauiie  point  of  its  oiUt,  shows  i^^  mm- 
meiii  the  swarm  at  the  same  point  in  sneoesaive  yeeis. 
AU  tlw  mete(»dds  of  tibe  swarm  mnst  of  oonrse  he  moving 
in  the  aamodiieetion,  else  they  would  soon  be  widely  Mat- 
tered. This  awtion  is  eonneeted  with  the  raiimi  point, 
•r  wdl-mednd  feetnie  of  a  meteocie  siiower. 


883 


ASTRONOMY. 


BadlMUt  Folnt.--BuppoM  that,  during  »  metaoric  shower,  we 
mark  the  path  of  each  meteor  on  a  atar  map.  as  in  the  tigure.  If  we 
continue  tne  pttldu  backward  in  a  atraight  line,  we  ihall  find  that 
they  all  meet  near  one  and  the  tame  point  of  the  ccleatial  sphere— 
that  is,  they  nore  as  if  they  all  radiated  from  this  point.    The 


Ite.  100.— SAMUR  Mora  c«r  namnuo 

laiHer  fa,  tfcewfow,  calkd  tta rmitmi  ftbd.    1  th*%BMl0MttMi 

do  Bo4  an  pais  aocoratalj  through  the  sane  point    TUitif  owing 

to  Urn  nnaraMaMi  man  —da  ft  ssaililiig  nnSt  the  psilL 

It  fa  found  that  tHe  i«dfaat^p(ibit  fa^^ahnys  in  the  sHMffoittioa 

the  stars,  wharever  the  obaerver  may  be  ritoatad,  and  that 


MSTKOm  AND  G0MKT8. 


883 


e  ahower,  we 
Igura.  If  we 
Mil  find  that 
itUl  sphere- 
point.    The 


TU|J«  owing 


iat«d,ind  tiMt 


it  does  not  partako  of  the  diuraal  motion  of  the  earth — that  is,  as 
the  stars  apparently  move  toward  the  west,  the  radiant  point  mores 
with  tltem. 

The  radiant  point  is  dne  to  the  fact  that  the  meteoroids  which 
strike  the  earth  during  a  shower  are  all  moving  in  the  same  direc- 
tion. If  we  sappose  the  earth  to  be  at  rest,  and  the  actual  motion 
of  the  meteoroias  to  be  compounded  with  an  imaginary  votbn 
equid  and  oppodte  to  that  of  the  earth,  the  motion  of  these  in 
inaiy  bodies  will  be  the  same  as  the  actual  relhtive  motion  of 
muteoroids  seen  from  the  earth.  These  relative  motions  will  all 
panllel ;  hence  when  the  bodies  strike  our  atmosphere  the 
dewsribed  by  them  in  their  passage  will  all  be  parallel  b(  _ 
linaa.  Now,  by  the  principles  of  spherical  trigonometry,  a  stmi^ 
lin«  seen  by  an  observer  at  any  point  is  projected  as  a  great  elrcj^ 
of  the  celestial  sphere,  of  which  the  observer  suppoees  hiiaself  to  |^ 
the  centre.  If  we  draw  a  line  from  the  observer  parallel  to  tap 
paths  of  the  meteors,  the  direction  of  that  line  will  repteaent  a  pobli 
of  the  sphere  through  which  all  the  paths  will  seem  to  pass ;  tili 
wiU,  therefore,  be  the  radiant  point  in  a  meteoric  diower.  '*' 

A  slightly  different  conception  of  the  poUem  may  be  formed 
by  oonceiiHing  the  plane  passing  through  the  observer  and  contain- 
ing the  path  of  the  meteor.  It  is  evident  that  the  different  PlMws 
formed  by  the  parallel  meteor  paths  will  all  intonnct  eadi  other  in 
a  line  drawn  from  the  observer  parallel  to  this  path.  Tbla  line 
will  then  intersect  the  celestial  sphere  in  the  radiant  point. 

Orllita  ofKatoOEie  Btaowers.— From  what  has  Jtut  becta  saM, 
it  vrill  be.seen  tiiat  the  position  of  the  radiant  p^t  indloatea  the 
direetliw  hi  which  the  meteoroids  move  rehtUvely  to  the  earth.  If 
we  also  knew  the  velocity  with  which  ihqr  m  r*i3^1  ■»▼%  *> 
space,  we  cooUl  taiake  allowance  for  the  motion  <rf  HMevtli,  iM 
tfoiirdatanaine  the  direction  of  their  actoal  motioa  in  ap^.  It 
willba  lemembeted  that,  as  just  ezplaiMd.  the  •;(««&€  «r  MAr 
tivl  notioB  it  made  up  of  two  oompoaenta— the  eoa  llja  Mtwl 
motkm  (rf  the  body,  the  other  the  mofiiM  of  the  e^jtaMiL  Ih  'm 
opporite  dinetkw.  We  know  the  aepond.of  thfes*  eMppOMnta 
abM^;  andi^we  kad^the  v«lMityi«lativ«  totMwtfli  m^ 


diraBMMiaa8ln|nbTth«Midiantp«dnt,we         .^ 
andflM«Mmoaeiitiaaagnitad«aBd  dintitkm.    Ilie  < 
of  the  other  eonponent  is  dne  (if  the  simplapt  preblwi 
matlea.    lima  we  ahaB  kwre  the  ttstoal  dIrefatiOB  and  v« 
theneteotkewamiaqiaee.    Having  this  direetlMi  and ' 
th«  («l|lt  ef  IN  ftnmmMmA  the  son  admita  pf  Niog  cale 

ITiltttnm'  of  MMian  waA  Ottatis.-— The  tdtoiBi^ol'^ 
meteorokb  does  not  admit  of  being  determined  from  ob^ 
servation.  One  element  neoeiBeiy  for  determining  the 
orbits  of  theM  bodies  is,  therefore,  ^ranting.  In  13m  e«w 
of  the  showers  of  1799, 1888,  and  1866,  oemmMify  edlsd 
the  November  showen,  tids  ebment  is  gttml^  the  time 


WVi  i-wii*ti?.MWM<*ft.?fc^:'jIyjSj,^;'ii^i^ 


■WiyMi-kWWii^'fiW^^MiiPWggSai 


884  AamONOMT. 

of  revolntion  around  the  stm.  Since  the  ahowen  oconr  at 
intervals  of  about  a  third  of  a  century,  it  is  highly  prob- 
able this  is  the  periodic  time  of  the  swann  around  tiiesun. 
The  periodic  time  being  known,  the  velocity  at  any  dis- 
tance from  the  sun  admits  of  calculation  from  the  theory 
of  gravitation.  Thus  we  have  all  the  data  for  determining 
the  real  orbits  of  the  group  of  meteors  around  the  sun. 
The  calculations  necessary  for  this  purpose  were  made 
by  Lb  Yerrirk  and  other  astronomers  shortly  after  the 
great  shower  of  1866.  TIio  following  was  the  orbit  as 
given  by  Lb  Ybrrieb  : 

Period  of  revolution 88'Myeen. 

Eoeentrioity  of  orbit 0-MM4. 

Least  dletsnce  frou  the  nm OMM. 

InoUnstioii  of  orbit \W  W. 

Longitude  of  the  node 51*  18'. 

Position  of  the  perihelion  (near  the  node). 

The  publication  of  this  orbit  brought  to  the  attention 
of  the  world  an  extraordinary  coincidence  which  had 
never  before  been  suspected.  In  December,  1866,  a 
faint  telescopic  comet  was  discovered  by  Tbxpbl  at  Mar- 
seilles, and  afterward  by  H.  P.  Tuttlb  at  the  Kaval 
Observatory,  Washington.  Its  orbit  was  calculated  by 
Br.  Opfolzkr,  of  Vienna,  and  his  results  were  finally  pub* 
lished  on  January  28th,  1867,  in  the  Atironomi$eh»  Ifaak- 
riehtenf  they  were  as  follows : 

Period  of  revolution 88*18  vears. 

Bocentrteity  of  ort>it 0  •  90M. 

Least  distMioe  from  the  sna O'VKS. 

laelination  of  ori^ IM*  4*'. 

Longitude  of  the  node Sl'M'. 

lioa^tude  of  the  perihelioa 48*  84'. 

The  publication  of  the  oometaiy  orMt  014  that  of  the 
cnrbit  of  the  meteoric  group  were  nuuie  indepoidently  with- 
in a  few  days  of  each  other  by  two  aatronomam,  neither 
of  whom  had  any  knowledge  of  the  w<Mrk  of  the  other. 
Oomparing  them,  the  result  is  erident  The  marm*  <f 
tMUoroiig  vhieh  eaute  the  JTovemhtr  $howan  motw  ti» 
th*9am^  orbii  witK  TnmtL'i  comet. 


mmm 


lowers  oconr  at 
)  highly  prob- 
roondUiesiin. 
ity  at  any  dis- 
om  the  theory 
>r  determining 
mnd  the  ran. 
Me  were  made 
ortly  after  the 
the  orbit  as 

r~ 

0. 

[V. 

¥. 

the  node). 

the  attention 
ice  which  had 
nber,  1865,  a 
SMPn.  at  Mar- 
at the  Kaval 
I  oalonhtted  by 
are  finaUy  pnb- 
\<mitch«  Jfaak- 

iSlSjMn. 

LOOM. 

)Vns. 

ler  4r. 

n4  that  of  tiie 
pendentlywith- 
Korntn,  neitlier 
of  the  fliher. 
The  mamu  (f 
muen  motM  «» 


IHK  AUaUNT  MKT/COUS. 


385 


Trmi>kl*h  comet  passed  its  perihuHon  in  January, 
1860.  Tho  most  striking  meteoric  sliower  communced 
in  the  following  November,  and  was  repeated  during 
several  years.  It  seems,  therefore,  that  the  meteoroids 
which  produce  these  Hhowot«  follow  after  Teiipki/s  comet, 
moving  in  tho  same  orbit  with  it.  This  shows  a  curious 
relation  between  comets  and  meteors,  of  which  we  shall 
speak  more  fully  in  t)te  nuxt  chapter.  When  this  fact 
was  brought  out,  the  question  naturally  arose  whether  the 
same  thing  might  not  l)e  tmo  of  other  meteoric  showers. 

Other  Showen  of  Meteors* — Although  tho  Novcmlwr 
showers  are  the  only  ones  so  brilliant  as  to  strike  the  ordi- 
nary eye,  it  lias  long  been  known  that  there  are  other 
nights  of  the  year  in  which  more  shooting  stars  than  usual 
are  seen,  and  in  which  the  large  majority  radiate  from  one 
point  of  the  heavens.  This  shows  conclusively  that  they 
arise  from  swarms  of  meteoroidi  moving  together  around 
the  sun. 

August  MMeors. — The  best  marked  of  these  minor 
showers  occurs  about  Augnst  9th  or  10th  of  each  year. 
The  radiant  point  is  in  the  constellation  Per»eu».  By 
watching  die  eastern  heavens  toward  midnight  on  the  0th 
or  10th  of  August  of  any  year,  it  will  be  seen  that  numer- 
ous meteors  move  from  north-east  toward  south-west,  hav- 
ing often  the  distinctive  characteristic  of  leaving  a  trail 
behind,  which,  however, vanishes  in  a  few  moments.  As- 
suming their  orbits  to  be  parabolic,  the  elements  were  oal- 
cukted  by  Sohiapabklu,  of  Milan,  and,  on  comparing  with 
the  orbits  of  observed  comets,  it  was  found  that  these 
meteoroids  moved  in  neiriy  the  same  orbit  as  the  second 
comet  of  1863.  The  ^exiMit  period  of  this  oomet  is  not 
known,  although  the  orbit  is  certainly  elliptic.  Aooord- 
ing  to  the  best  oalenlation,  it  is  194  years,  but  for  reasons 
given  in  the  next  ibapter,  it  may  be  nnoertaift  by  ton 
yean  or  moire. 

Thsre  is  out  remafkable  dUhraice  between  the  iugnst  and  ths 
NoveMker  asefeon.    llw  latter,  ■■  we  have  seen,  appear  far  two 


^miim 


386 


ARTRONOMT. 


or  throe  conaecutlve  yMn,  und  then  are  not  Men  again  until  about 
thirty  yearn  have  elapaed.  But  the  August  metoon  are  leen  erery 
year.  This  showi  tliat  the  atream  of  Auguat  meteoroids  is  endleaa, 
everr  part  of  the  orbit  being  occupied  br  them,  while  in  the  caae 
of  tne  November  onea  they  are  nthered  into  a  group. 

We  may  conclude  from  this  that  the  Novemtor  meteoroidn  have 
not  been  permanent  memben  of  our  system.  It  is  beyond  all  prob- 
ability that  a  group  compriaing  countless  million*  of  such  bodies 
should  all  have  the  same  timu  of  revolution.  Even  if  they  had  the 
same  time  in  the  beginning,  the  different  actions  of  the  planeta  on 
different  parts  of  the  group  would  make  the  times  different.  The 
result  would  be  that,  in  the  course  of  ages,  those  which  had  the 
moat  rapid  motion  would  go  further  and  further  ahead  of  the 
others  until  they  got  half  a  revolution  ahead  of  them,  and  would 
ttnally  overtake  those  having  the  sloweat  motion.  The  swiftest  and 
slowest  one  would  then  be  in  the  position  of  two  race-horses  running 
around  a  circular  track  for  so  long  a  time  that  the  swiftest  horse 
has  made  a  complete  run  more  than  the  sloweet  one  and  has  over- 
taken him  from  oehind.  When  this  happens,  the  meteoroids  will 
bo  scattered  all  around  th«i  orbit,  and  we  shall  have  a  shower  in 
November  of  every  year.  The  f^  that  has  not  yet  happened  shows 
that  they  have  been  revolving  for  only  a  limited  length  of  tinte, 
probably  only  a  very  few  thousand  years. 

Although  the  total  mass  of  these  bodies  is  very  small,  yet  their 
number  is  beyond  all  estimation.  Professor  Nbwtok  has  estimated 
that,  taking  the  whole  earth,  about  seven  million  siiooting  stan  are 
encountered  every  twenty-four  hours.  This  would  make  between 
two  and  three  thousand  million  meteoitrfds  which  an  thus,  as  it 
were,  destroyed  every  year.  But  the  number  wliich  the  earth  can 
encounter  in  a  year  is  only  an  iudgnilloant  fraction  of  tlie  total 
number,  even  in  the  solar  system.  It  may  be  interesting  to  calculate 
the  ratio  of  the  space  swept  over  by  the  earth  in  the  coarse  of  a  yeiur 
to  the  volume  of  the  sphere  surrouiiding  the  son  and  nteading  out 
to  the  orbit  of  Ntotuns.  We  shall  find  this  ratio  to  be  oa^  m  one 
to  about  three  millions  of  milUoos.  If  we  meaaore  by  tiia  Bomber 
of  meteoKrids  in  a  euMc  mile,  we  mla^t  oonrfdar  theSii  very  thinly 
scattered.  Then  ia,  in  fact,  only  a  wigle  meteor  to  aevmnal  million 
cuUe  kilometres  of  space  iin  the  heavens.  Tet  the  to^  number 
is  immensely  great,  because  a  globe  including  the  orUt  of  l!l(^fititme 
would  contain  millions  of  millions  of  mllUoas  of  millions  of  cubic 
kilometres.*  If  we  reflect,  in  addition,  that  the  meteoroids  probably 

*The  compotathma  leading  to  this  nsnlt  naj  be  mads  in  the  fd- 
knrhur  manner: 

I.  TttfinithaeUbuatifaM  mmptO^tmgk  JyAssafAAi  tiU  tawnnf 
at/ear.  If weput irforthentfoof thedraoafereiiMoraclndetolts 
dfcuneler,  and  p  for  the  nKlins  of  the  eaithtttiasarflMW  of  aplaaescetiM 
of  the  earth  passing  thraoii^  lu  centre  wIO  bs  «^.  Mvmtijlng  tUa 
by  the  droumferenoe  of  the  earth's  orbtt,  we  shall  have  the 
quired,  whkli  we  readil|y  And  to  he  more  than  W.OM  i 
minions  of  kihNMtres.  BfaMM,  in  sweepbig  throiuh  tMs 
earth  enoounteni  shoot  9Bto  mJUDns  of  meteoroids.  it  ' 


sn  again  until  about 
ftoon  are  seen  erery 
leteoroids  ii  endleea, 
1,  while  in  the  cam 
group. 

ber  Bieteoroids  have 
t  it  beyond  all  prob- 
lions  of  such  bodieo 
STcn  if  they  had  the 
ni  of  the  planeta  on 
imet  diHerent.    The 
hoae  which  bad  the 
urther  ahead  of  the 
of  them,  and  would 
n.    The  twiftert  and 
)  raee-horaea  running 
tt  the  Bwifteat  hone 
■t  one  and  baa  orer- 
,  the  meteoroida  will 
«H  have  a  shower  in 
t  yet  happened  ahows 
lited  length  of  time, 

I  very  nnaU,  yet  their 
[■WTOM  has  eatioMted 
lion  shooting  stars  are 
would  make  between 
which  are  thus,  as  It 
which  the  eartii  can 
fraction  of  the  total 
intereetingtocftkulate 
In  the  ooorse  of  a  year 
Hin  and  octeading  out 
«tioto  beoBlyaaone 
eaaore  bj  tlw  Bomber 
dder  themT«rythiiily 
itflor  to  several  muiion 
ret  tiie  to^  number 
S  the  orUt  of  Kt^tMrn 
»  of  ndlUona  of  oubio 
ke  meteonrfds  probably 

US  be  made  fai  the  f  ol- 
ifenoMotadHdetota 

ba&  have  the  «»•  m- 
km  80.000  mfHoiiB  of 


wilfcL.1    .-^.■zliW.lBB.aii'^SJJtW!".''*!"!      ''  "*; 


THE  ZOUtACAL  LIOIIT. 


387 


on- 


welghbttta  few  grains  each,  we  ihallseo  how  it  istliattboy  aru 
tirely  invisible  to  vision,  even  with  powerful  telescopes. 


The  Sodiaoal  Light. — ^If  we  observe  tho  westeni  nVy 
during  the  winter  or  spring  montlis,  al)out  the  end  of  tho 
evening  twrilight,  we  shall  see  a  Btream  of  faint  light,  a 
little  like  tho  Milky  Way,  rising  oliliquely  from  tho  west, 
and  directed  along  the  eoliptio  toward  a  point  south-wcHt 
from  the  zenith.  This  is  called  the  zodiacal  light.  It 
may  also  be  seen  in  the  east  before  daylight  in  the  morn- 
ing daring  the  autumn  months,  and  has  sometimes  lieen 
traced  all  the  way  across  the  heavens.  Its  origin  is  still 
involved  in  obscurity,  but  it  seems  probable  that  it  arises 
from  an  extremely  thin  cloud  either  of  meteoroids  or  of 
Bemi-gasoons  matter  like  that  composing  the  tail  of  a 
comet,  spread  all  around  the  sun  inside  tho  earth's  orbit. 
The  researches  of  Professor  A.  W.  Wbioht  show  that  its 
spectrum  is  probably  that  of  reflected  sunlight,  a  result 
which  gives  color  to  the  theory  that  it  arises  from  a  cloud 
of  meteoroids  revdTing  round  the  sun. 

there  is  only  one  meleoioid  to  more  than  ten  millions  of  cubic  kil- 


iKe$paiitmef*fkroiigklgih»tartkina 


Let  us  put  r  for  the  ^- 


maoo of  Seearth  from  the  sun.  Then  the  distance  of  Neptune  may 
be  taken  as  80  r,  and  this  wiU  be  the  radius  of  the  sphere.  The  cir- 
cumference of  the  oarth'a  orbit  will  than  be  8  irr.  and  the  space  swept 
over  wUl  be  9  «•  r  «i^.    The  aphere  of  Neptun*  will  be 


I  ir80»  f»  =  86,000  «•  r»,  nearly. 


Tlie  ratio  of  the  two  i 


I  will  be 


18.000  f* 


8.000 


,  nearly. 


The  ratio  -  ia  mote  than  98.000,  showing  the  required  ratio  to  be 

about  three  millioM  of  mUlioM.    The  totol  number  of  seattend  mete- 
ondda  la  tbmfore  to  be  redraoed  by  ndllkma  of  mlllkma  of  milliona. 


Wl*?^faMMMPte9K%^f^|^[^^ 


i! 


CHAPTER    XIII. 

I 

COMKTS. 
^  1.    ABPBOT  OF  CX)1I1T8. 

CoMfTTH  are  <UHtingiu»h«<l  from  the  plancte  l>otl»  by  their 
agpecte  and  their  ..u»ti«,nB.     They  come  into  view  w.t^iout 
anything  to  herald  their  approach,  continue  in  wght  f..r  a 
few  weeks  or  months,  and  then  gradually  vanwh  in  the 
distance.     TUey  are  commonly  considered  a*  co»npo«od  of 
three  parts,  the  nudeu*,  the  cmui  (or  hair),  and  the  tml. 
The  nucleus  of  a  ooiiiet  is,  to  the  naked  eye,  a  point  of 
light  resembling  a  star  or  planet.     Viewed  in  a  teWpe, 
it  generaUy  has  a  small  disk,  but  shades  off  so  graduaUy 
tliat  it  is  difficult  to  estimate  ite  magnitude.     In  hu^ 
comets,  it  is  sometimes  several  hundred  miles  in  diameter, 
but  never  approaches  the  size  of  one  of  the  larger  planets. 
The  nucleus  is  always  surrounded  by  a  mass  of  foffljy 
liirht,  which  is  called  the  eama.    To  the  naked  eye,  the 
nucleus  and  coma  together  look  like  a  star  seen  through  a 
mass  of  thin  fog,  which  surrounds  it  with  a  sort  of  halo. 
The  coma  is  brightest  near  the  nucleus,  so  that  it  is  hardly 
possible  to  tell  where  the  nucleus  ends  and  whero  the 
Soma  begins.     It  shades  off  in  every  direction  so  gradually 
that   no  definite  boundaries  can  be  fixed   to   it.     Ohe 
nucleus  and  coma  together  are  generally  called  the  head 

of  the  comet.  ...        t  »i.a 

The  taU  of  the  comet  is  simply  a  continuation  of  the 
coma  extending  out  to  a  great  distance,  and  always  di- 
,«cted  away  from  the  sun.  It  has  the  appearance  of  a 
stream  of  milky  light,  which  grows  fainter  and  broader 


rwrnn'msm^" 


ASl'KVr  Of  VO.VKTH. 


381) 


uta  lK)th  by  their 
ito  view  without 
no  in  fliglit  for  a 
ly  vanish  in  the 

as  oompoflod  of 
r),  and  the  tail. 

eye,  a  point  of 
d  in  a  t«loBcopo, 
off  80  gradually 
itude.  In  largo 
nilea  in  diameter, 
lie  larger  planets. 
M  nuM  of  foggy 
0  naked  eye,  the 
it  seen  through  a 
\i  a  sort  of  halo. 

0  that  it  is  hardly 
3  and  where  the 
Btion  so  gradually 
led  to  it.  The 
r  called  the  Kead 

atinuation  of  the 
B,  and  always  di- 

1  appearance  of  a 
inter  and  broader 


iiM  it  ruciMlt  from  titu  liuud.  Lilcu  tltu  count,  it  HliadeH  oti 
HO  ^niduully  tliiit  it  itt  iinpoHMllilu  to  fix  iiiiy  iNMiiMlariuH  to 
it.  Till)  li)ii;;th  ot  tlir  tiiil  variuH  fnnii  '2^  or  l\°  to  W"  «»r 
more.  Uuiiurally  thu  nioru  orilliaiit  tliu  liuad  of  tliu  coiitut, 
tliu  loii^c'iitHl  Itriglii  riri  thu  tail.  It  iHalHo  uftuii  hriglitor 
and  nioru  Mwirply  dutinud  at  onu  cdgu  tlian  at  tliu  othur. 

Tliu  alMivu  dt'M-riptioii  appliuH  to  iM>inut«(  which  can  Ih) 
plainly  ttuuii  by  thu  iiakud  uyu.  After  ii^ti'uiioiuurH  Intgaii 
to  (iwuup  thu  liuavuns  carefully  with  tuluMCoputt,  it  watt 
found  that  many  comuts  caiiiu  into  Hight  which  would 
uiitirely  e8ca))u  thu  unaided  viHioii.  TIiuhu  aru  called  tel- 
f«atj>ic  mmeUi.  Homutimes  hIx  or  muru  of  hucIi  comutH  aru 
discovered  in  a  siiiglu  yuar,  wliilu  oiiu  of  thu  brighter  claut 
may  not  be  6uo>t  for  ten  years  or  mure. 


Fio.  101. 


lOOlUR 
OUT  A  MUOLBVB. 


;-     VJn.lOB.— VBLMCWPIOOOMBT 
WITH  A  NUOLBUa. 


When  comets  are  studied  with  a  telescope,  it  is  found 
tluit  they  are  subject  to  extraordinary  changes  of  structure. 
To  understand  these  changes,  wo  must  begin  by  saying  that 
comets  do  not,  like  the  planets,  revolve  around  the  sun  m 
nearly  oironlar  orbits,  but  always  in  orbits  so  elongated 
that  tiie  oomet  is  visible  in  only  a  very  small  parf  of  its 
oonne.  When  one  of  these  objects  is  first  seen,  it  is  gen- 
erally approaching  the  sun  from  the  celestial  spaoes. 
At  this  time  it  is  nearly  always  devoid  of  a  tail,  and  some- 
times of  a  nucleus,  presenting  the  aspect  of  a  thin  patch 
of  cloudy  light,  which  may  or  may  not  have  a  nucleus  in 


390 


ASlTtaJrOMY. 


its  centre.  Ab  it  approaches  the  sun,  it  is  generally  seen 
to  grow  brighter  at  some  one  [)oint,  and  there  a  nucleus 
gradually  forms,  being,  at,  iirst,  so  faint  that  it  can  scarcely 
be  distinguished  from  the  surrounding  nebulosity.  The 
latter  is  generally  more  extended  in  the  direction  of  the 
sun,  thus  sometimes  giving  rise  to  the  erroneous  impres- 
sion of  a  tail  turned  toward  the  sun.  Continuing  the 
watch,  tlie  true  tail,  if  formed  at  all,  is  found  to  liegiii 
very  gradually.  At  first  so  small  and  faint  as  to  be  almost 
invisible,  it  grows  longer  and  brighter  every  day,  as  long 
as  the  comet  continues  to  approach  the  son. 


g  2.    THE  VAPOBOTTS  JDfVELOFEB. 

If  a  comet  is  very  small,  it  may  undergo  no  changes  of 
aif«pect,  exc^  then  just  described.  If  it  is  an  unusually 
bright  one,  the  Bext  object  noticed  by  tdeieqyie  examina- 
tion wOl  be  B  b<»ir  ■anrounding  ihe  nodeas  on  the  side 
toward  the  ton*  T\a»  bow  wiU  gradwlly  rise  up  and 
spread  o||l4n  afl  ridWy  finally  alMimbig  tiw  fonn  of  a 
semicjieteliiviig  tii»  Imoleng  in  Hieaalie,  or,  to  speak 
with  mora  jtieeiSon,  tiie  form  of  s  jHrnbda  i»Ting  the 
nucleus  near  Ma  loens.  The  two  etiik  tf  ^  parabola 
will  extend  out  fnrther  and  further  so  as  to  form  a  part 
of  the  tail,  and  finally  be  lost  in  it.  Oontinning  the 
watch,  other  bows  will  be  found  to  form  around  the  nn- 
clens,  all  slowly  rising  from  it  like  «douds  of  vapor. 
These  distinct  vaporous  masses  are  called  the  etwdopet : 
they  sbsde  off  gradually  into  the  ooma  so  as  to  be  with 
difficulty  distinguished  from  it,  and  indeed  may  be  con- 
sidered as  part  of  it.  The  inner  envelope  is  sometimes 
connected  with  the  nudens  by  one  or  more  fan-shqied 
appendages,  the  centre  of  the  fan  being  in  the  nnelens, 
and  the  envelope  forming  its  round  edge.  This  a^iear- 
ance  is  apparently  caused  by  masses  of  wpat  streaming 
up  from  that  nde  of  the  nudens  nearest  the  son,  and  grad- 
oally  spreading  around  the  comet    on  eadi  aide.     Hie 


ENVELOPES  OF  00MET8. 


■  -J 
891 


generally  seen 
there  a  nucleus 
it  can  scarcely 
bulosity.  The 
irection  of  the 
moouB  impres- 
^ontinuing  the 
'onnd  to  liegin 
as  to  be  almost 
ry  day,  as  long 


)  no  changes  of 
is  an  nnuBually 
letq^ksexaniina- 
«B  on  ihe  side 
ly  riM  up  and 
^  fofm  of  a 
«,  ottfU*  speak 
da  iMiving  the 
f  0k  purabok 
to  form  a  part 
Dontinning  the 
around  the  nit- 
udiK   of   vapor. 
i  the  envelope*  : 
0  M  to  be  with 
3d  may  be  con- 
w  i«  sometimes 
dore  fan-shaped 
in  the  nnoleos, 
.    This  aj^iear- 
rupor  streaming 
teson,  and  grad- 
Mk  aide.     Tko 


form  of  a  bow  is  not  the  real  form'  of  the  envdopcs,  but 
only  the  apparent  one  in  which  we  see  them  projected 
against  the  background  of  the  sky.  Their  true  form  is 
similar  to  that  of  a  paraboloid  of  revolution,  surrounding 
the  nucleus  on  all  sides,  except  that  turned  from  the  sun. 
It  is,  therefore,  a  surface  and  not  a  line.  Perhaps  its  form 
can  be  best  imagined  by  supposing  the  sun  to  bo  directly 
above  the  comet,  and  a  fountain,  throwing  a  liquid  hori- 
zontally on  (dl  sides,  to  be  built  upon  that  part  of  the 
comet  which  is  uppermost.  Such  a  fountain  would  throw 
its  water  in  the  form  of  a  sheet,  falling  on  all  sides  of  the 
cometic  nucleus,  bat  not  tonching  it.  Two  or  three  vapor 
surfaces  of  this  kind  are  sometimes  seen  around  the  comet, 
the  outer  one  ^jf^oAkg  each  of  the  iimer  <»cs,  but  no  two 
tonching  eadtililL 


WiB.  IM.— voBHAnoir  oi^ 


To  give  a  dlM>  conoBptlon  of  the  lonpetkm  sad  iDotimi  of  the 
envdoiwi,  we  p>lSBt  two  ilgares.  tiie  lint  of  these  rtMms  the  q^ 
pewanoe  of  tiie  eavdopes  m  four  •ueoeariTe  iteges  of  their  eourw, 
and  anr  be  rqpaded  as  seedoas  of  the  vesl  mabteUxhsped  mr- 
fwMS  wMch  flwj  tesm.  In  all  tiiese  fgores,  the  mib  b  ami^fiimi  to 
be  sboTO  tbe  oobmI  in  the  figure,  sad  the  tail  of  the  oomet  to  be 
dinged  dowsamad.  Id  •  the  riM«t  ct  vapor  has  jnat  besoa  to 
titk  la  >  It  ii  fiiea  aad  expaaded  yet  farther.  la  <  ii  has  B«nm 
to  aove  aw«r  a*id  mm  agovad  tine  oooiet  oa  aU  lidee.  "  naally, 
in  d  this  Ian  bm^mi  1mm  ooae  lo  far  that  the  higher  portkHW 
have  aesiijr  disaroeared,  me  larger  part  of  the  awtter  havinig 
moved  awav  toirwd  tha  taiL  Before  the  st^^e  «  is  raaohsd,  a 
■eooad  mrmofm  will  eoauaoa^  b^a  to  rise  as  at  «,  ao  iltat  two 
or  thsee  aaiy  be  virfUft  at  the  nune  tfaae,  encloaed  within  eseh 


la  tiM  next  figure  the  actual  motioa  of  the  matter  oompos- 


mm 


in 


ASTRONOMY. 


ing  the  eavclo|)c8  \s  shown  by  the  courses  of  the  several  dotted 
lines.  This  motion,  it  will  be  seen,  is  not  very  unlike  that  of 
water  thrown  up  from  a  fountain  on  the  part  of  the  nucleus 
nearest  the  sun  and  then  falling  down  on  all  sides.  The  point  in 
which  the  motion  of  the  cometio  matter  differs  from  that  of  the 
fountain  is  that,  instead  of  being  thrown  in  continuous  streams, 
the  action  is  intermittent,  the  fountain  throwing  up  successive 
sheets  of  matter  instead  of  continuous  streams. 

From  the  gradual  expansion  of  these  envelopes  around  the  head 
of  the  comet  and  the  continual  formation  of  new  ones  in  the  im- 
mediate neighborhood  of  the  nucleus,  they  would  seem  to  be  due 
to  a  process  of  evaporation  going  on  from  the  surface  of  the  latter. 
Bach  layer  of  vapor  thiu  formed  rises  u|>  and  spreads  out  con- 
tinually until  the  part,  next  the  sun  attains  a  certdn  maximum 
height.  Then  it  gradually  moves  away  from  the  sun,  keeping  its 
distance  from  the  comet,  at  leaat  until  it  passes  the  latter  on  every 
side,  and  contiaues  onward  to  form  the  tuL 


Fio.  101— imuutioK  or  omanrVi  taou 

Theak  jAeaomem  w«n  felly  obwrvad  ia  tiM 
18U,  «fee  obaervatiiMM  of  wfcMi  w«n  ciMMIIr 
M4lPMif«HbrBgiii>,^r     " "^ 

^MM  ^fln*  'ttOVM 


•«d  the  iuMT  oiM  <*.    f 

aoth  tx  «  ImI^  «f  fdNMi  1'. 

%liM^  lonwur,  ■ItMrdluid  tmmmL  ilMciaeawl  r 
%ipHk(M<  w  M  to  tikif  th*  |ttm«l  Am  Int 
«i»<lofwi  ia  ril  wan  Mw  to  An  fnMtUi«««|BL4w|M 
men^  on  October  MA,  whni  all  Am  often  M  Mm  ^UtitH^iiiMk. 
The  Mto  at  idiiA  Mm  envelopea  aneaiM:  mw  g«MMd|jr  Imw  f#  to 
60  Uiometna  par  Imw,  the  ordinary  ONed  4rf  ft  nttwnr^nin. 

The  flm  OM  roM  to  a  hdglit  of  abottft  aO^OOO  IdlWMlm,  bat  it 
WM  flnally  ^Sfaalpatod.  Bat  the  mooearive  eaea  ^^mmammH  at  • 
lower  and  lower  elevation,  the  sixtb  brtur  loat  ai^t  of  at  •  heirtit 
of  about  10^000  kilonetraeu 


.Uffttl.WllWl.'WjliNeyri  II I  H|[j^.WiiWtViv-r*-v  xx»*;^qi«Ki>-^ 


The  mmofrn'^iimt 


^itMWIUWMlte 


Boveral  dotted 
unlike  that  of 
>f  the  nucleus 

The  point  in 
om  tliut  of  the 
nuous  streamg, 

up  successive 

'ound  the  head 
ones  in  the  im- 
seem  to  be  due 
Be  of  the  latter, 
ireads  out  con- 
rtain  maximum 
tun,  keeping  its 
I  bitter  on  every 


8PE0TRA   OF  COMETS. 


393 


IL. 


■MOlyCmnMle 
llwnp4nlB. 
JloMtm,  bal  ft 

hlMataheli^ 


In  the  great  comet  of  1861,  eleven  envelo])e8  were  seen  between 
July  3d,  when  portions  of  three  were  in  sight,  and  the  19th  of 
the  same  month,  a  new  one  rising  at  regular  mtervals  of  evenr  sec- 
ond day.  Their  evolution  and  dissipation  were  accomplished  with 
much  greater  rapidity  than  in  the  case  of  the  great  comet  of  18S8, 
an  envelope  requiring  but  two  or  three  days  instead  of  two  or  three 
weeks  to  paaa  through  all  its  phases. 


8  8.    THE  PHTSIOAL  OOlTSTrFUTIOir  OF  OOKBTS. 

To  tell  exactly  what  a  comet  is,  wo  should  be  able  to 
show  how  all  the  phenomena  it  presents  would  follow  from 
the  properties  of  matter,  as  we  learn  them  at  the  surface 
of  the  earth.  This,  however,  no  one  has  been  able  to  do, 
many  of  the  phenomena  being  sneh  as  we  should  not  ex- 
pect from  the  known  constitution  of  matter.  All  we  can 
do,  therefore,  ii  to  present  the  principal  eharacteristics  of 
comets,  as  shown  by  ofaiervation,  and  t»  explain  what  is 
wanting  to  rewmeile  these  ehancteristieB  with  the  known 
properties  of  nuttter.      i    i  •!^\ 

In  the  first  place,  idl  eomets  which  )a»r«  been  examined 
with  the  spedMieope  diow  a  speetnim  otnnposed,  in  part 
at  least,  of  bright  llnea  or  baa^  These  Knee  have  been 
supposed  to  be  identified  wiA  those  of  carbon;  but 
although  the  similarity  ci  aqieot  ia  Tetryatrildng,  the  idm- 
tiity  cannot  be  regaided  aa  pnyven. 


:nPk'Mlb« 


bi  Hie  anHBced  flgoM  flw  vipfn  tfmktm.  A,  it  ihat  of  onlMm 
tak«iiaolc«aBt»[kaBdth«l9w«roB«,B,«|MtofaeoaMt  TImm 
raeotra  te««rpNt«d  la  Ami  umal  way  would  iadioite,  flntly,  that 
the  conit  isaaawNia;  teooadly,  that  the  gwes  wUdh  compotfs  it 
are  so  hot  as  to  ridae  by  their  own  U^t,    But  we  cannot  admit 


804 


A8TR0N0MT. 


these  interpretations  without  bringing  in  some  additional  theory. 
A  mass  of  gas  surrounding  so  minute  a  body  as  the  nucleus  of  a 
telescopic  comet  would  expand  into  space  hj  virtue  of  its  own 
elasticity  unless  it  were  exceedingly  rare.  HoreoTer,  if  it  were 
incandescent,  it  would  speedily  cool  off  so  as  to  be  no  longer  self- 
luminous.  We  must,  therefore,  propose  some  theory  to  account 
for  the  continuation  of  the  lumfnonty  through  numy  centuries, 
such  as  electric  activity  or  phosphorescence.  But  without  further 
proof  of  action  of  these  causes  we  cannot  accept  their  reality.  We 
are,  therefore,  unable  to  say  with  certainty  now  the  light  in  the 
spectrum  of  comets  which  produces  the  bright  lines  has  its  origin. 


In  the  last  chapter  it  was  shown  that  swarms  of  ininuto 
])urticles  called  meteoroids  follow  certain  comets  in  their 
orbits.  This  is  no  donbt  true  of  all  comets.  We  can  only 
regard  these  meteoroids  as  fragments  or  debris  of  the 
oomet.  The  latter  has  therefore  been  considered  by  Pro- 
fessor Nkwton  as  made  up  entirely  of  meteoroids  or  small 
detached  masses  of  matter.  These  masscis  are  so  small  and 
so  numerous  that  they  look  like  a  dond,  and  the  light 
whidt  they  reflect  to  our  eyes  has  tiie  milky  i4)pearanoe 
peculiar  to  a  omnet  On  tlus  theory  a  telescopic  comet 
which  has  no  nucleus  is  simply  a  doud  of  these  minute 
bodies.  The  nudeus  of  the  brighter  comets  may  either 
be  s  more  condensed  mass  of  such  bodies  w  it  noay  be  a 
solid  w  liquid  body  itsdf. 

If  the  reader  has  auy.difflonlty  in  reoondling  this  theory 
of  detached  pariides  with  the  view  already  presented, 
tluH  tkit  Hn^ilepai  teon  v^^iii  Hm  tail  ^.Hn  «oaiet  is 
lummA  oouiil  «if  hg^en  of  ivpoi^  ka  ttoat  Mmen^Mr  thai 
MiMia,  aiiah  aa  QlMd%  &f  ,  and  aniol%  «m» 
9y  composed  of  minute  separate  partides  of  watfM^  or 


«r  tt«  Oooaara  «BiL— Tbe  taS  <tf  iba 
it  not  a  poniMBMttt  appendago,  not  ia  eompoaed  of  tin 
masses  of  vapor  whidi  we  have  ahready  deaoribed  as  aa- 
oending  from  the  nudeos,  and  afterward  moving  away 
from  tiie  sttn.  The  tail  whidi  we  see  on  one  evening  is 
not  abeolutdy  the  same  we  saw  the  evening  before,  a 


•  n-'-sxjj»t«M»»niasaSB««B«nt*<««*4rt*a:-: 


gE'iiniiiiwiBwiiii'iri  II I iBwiiMiiiflKi 


litionsl  theory. 
ke  nucleus  of  a 
ue  of  its  own 
rer,  if  it  were 
no  longer  self- 
ory  to  account 
lany  centuries, 
rithout  further 
ir  reality.  We 
ie  light  in  the 
B  has  its  origin. 

ns  of  minute 
mets  in  their 
We  can  only 
Uhrig  of  the 
lered  by  Pro- 
roids  or  small 
)  80:  sniall  and 
Old  the  light 
:y  i^pearanoe 
secopic  comet 
these  minute 
ts  may  either 
•r  it  may  be  a 

ng  tiiie  theory 
iy  presented, 
ttW  OOOMt  is 

as  of  wat^r  or 


MOTIONS  OF  COMETS. 


395 


L<rf«lM 

ipowl  el  liw 
Miibed  as  as- 
moving  away 
>iie  evening  is 
dng  before,  a 


poiiiion  of  the  latter  having  been  dissipated,  while  new 
matter  has  taken  its  place,  as  with  the  stream  of  smoke  from 
a  steamship.  The  motion  of  the  vaporous  matter  which 
fonns  the  tail  being  always  away  from  the  sun,  there 
seems  to  be  a  repulsive  force  exerted  by  the  sun  upon  it. 
The  form  of  the  comet's  tail,  on  the  supposition  that  it  is 
composed  of  matter  thus  driven  away  from  the  sun  with 
a  uniformly  accelerated  velocity,  has  been  several  times 
investigated,  and  found  to  represent  the  observed  form  of 
the  tail  so  nearly  as  to  leave  little  doubt  of  its  correctness. 
We  may,  therefore,  regard  it  as  an  observed  fact  that  the 
vapor  wUch  rises  from  the  nucleus  of  the  comet  is  repelled 
by  the  ran  instead  ol  being  attracted  towaid  h,  as  larger 
masses  of  mattw  WPS. 


I  force'  1am 


ever  been 

1  in  its 

UlalllB  attoac- 

by  their 

'%o  one  of 

of 

titWilaponthe 

entireh 


No  iAafMto  emit— ttott  of  tUa  nohiMtc 
given.    H  ]N%  iHdad^  iMtt  tmgirtiiiit  tlit 

oluuaol|if^'lii!iiliia>^«B0'.'Wi:|p^: 

electriilSlS   K  &  KMNrMMv  «M 

the  nMH.MlMil  |(Mmw>i  BWiairtsil  tiflr^ 

oomet%,-  Jwl||iS|aii'^ 

oonwtVtW  Jt  ti>  W  MSMAit  a»  ^.WIHWWMWI  tHi  entirely 

iK>Iate|'l|pi^Mpyt  taf  tn-^acmk  snMitii|Mt  Jiiiy  liliiit^stiwhred 
fact  of     ^ 

In 
coDwta 
phyrio%        _^^ 

■■WbO  WfppNP:- N||R|||^,lMnKd  BB  QV  -'w 

If  iiAM'ml^^imm^ii^it^immi^wi***^ 

of  eonnta  mu  W«  koow  iriuit  fonaa  awttar  n 
diiemrt  itaok  tlUMawe  And  it  to  hav«  aaauJMd'in  oar  labota 
tt^jjes.     Thia  ia  a  question  whidi  we  merely  angaeat  wUhooi 
attempdiw  to  apecolato  optm  It.    R  can  be  answenu  onty  by  ex- 
perintnitd  neeanAea  in  dieiiiiatry  and  i^ysica. 


g  4.    MOVIOIIS  OV  OUMJm. 

Previow  to  the  time  of  KxwroNy  no  certain  knowledge 
respecting  the  aetnal  motions  of  comets  in  tho  heav«DS 
had  bean  aoqnired,  except  t^  they  did  not  move  aionnd 


396 


ABTRONOMT. 


the  snn  like  the  planets.  When  Newton  invefltigatod  the 
mathematical  rosnlts  of  the  theory  of  gravitation,  he  found 
that  a  body  moving  nndor  the  attraction  of  the  sun  might 
describe  either  of  tlie  throe  conic  sections,  the  ellipse,  par- 
abola, or  hyperbola.  Bodies  moving  in  an  ellipse,  as  the 
planets,  would  complete  their  orbits  at  regular  intervals 
of  time,  according  to  laws  already  laid  down.  But  if  the 
body  moved  in  a  parabola  or  a  hyperbola,  it  would  never 
return  to  the  sun  after  once  passing  it,  but  would  move  off 


It 


"Wtti,  lW.^4n>iimio  MMD 


to  infinity.  It  was,  therefore,  very  natoral  to  qondude 
that  comets  might  be  bodies  which  resmnble  the  plan^  in 
moving  under  the  sun's  attraction,  but  which,  instead  of 
describing  an  oKipse  in  regular  poriods,  lilce  the  phmeCs, 
move  in  parabolic  or  hyperbolic  orbits,  and  ther^ore 
<mly  approadk  the  bub  a  angle  time  duing  their  wh(^ 
existence.  ' 

UtiB  theory  is  now  known  to  be  essentially  tme  int 


aatmt 


wum 


ORIilTS  OF  VOMKm. 


897 


iBtigatod  the 
)n,  he  found 
e  sun  might 
ellipse,  par- 
lipse,  as  the 
lar  intervals 
But  if  the 
i^ould  never 
lid  move  ofi 


to  oondnde 
tbe  pkn^  in 
h,  instead  iA 

the  phmeto, 
nd  iher^iffe 
%  ikuwt  wbofe 

idly  tone  hxt 


most  ot  Wwi  observed  comets.  A  few  are  indeed  found  to 
be  rovolviMjr  around  the  sun  in  elliptic  orbits,  which  differ 
from  tho8{'  of  the  planets  only  in  l)oing  nmch  more  eccen- 
tric. But  tli.>  greater  nmnbcr  which  have  been  observed 
have  receded  ?rom  the  sun  in  orbits  which  wo  are  unable 
to  distingaiBJt  ?rom  parabolAs,  though  it  is  possible  they 
may  be  extillaely  elongated  ollipsee.  Comets  are  thwe- 
fore  divided  i/f^h  respects  their  motions  into  two  claaies : 
(1)  periodic  vknete,  which  ve  known  to  move  in  ellipiio 
orbits,  and  tf^um  to.the  «an  at  fixed  intervals  ;  and  (9) 
farahdio  otmO^  a||fMM^jr  aMviag  in  panbdflw,  ntver 
to  return.        ^ 

Tlie  first  ditfbperjr  el  Hi*  |»«liodWty  «f  a  ,«««« Vas 
made  by  ISiKum  vai ,*lmmiiAm  with  «be  gretfft^ei»l^i|  of 
1682.    K»«^ tl»>forfi ^  iilaiM II Am, iHit Jimd 
that  a  oonwimving  in  mn^  ^  <iM|tt.iuai>lt  wtllritttet  of 
1682  had «eJHN>en  ill  -^..Ml^  V^fljim'WSi&X. 
He  was  tfieil^  ^  to {^oeii^^ioii  tlm-^i,...,        _ 
comets  WiMl^ally  <!ihe  andf  Hie  same  olijeet,  i«tiii^&  to 
<>vik^  of  about  t5  or  t6  yeus.     He  tfaibre- 
itliMitWOnld  appevr  iigain  about  ^year 
BVck  a  pawdietion  rei^t  be  a  year  or  nwre  in 
to  the  effect  of  the  i^traction  of  the  phutets 
upon  the  ilinet.    In  the  mean  time  the  methods  of  calcu- 
lating tl^  ttttraotion  ^i  the  Janets  were  m>  f«r  in^roved 
that  it  biiiiMsM  pooBi^le  tomake  a  more  aeonn^e  fHfedic- 
iioUi    A«^^yeMr  1759  approached,  the  necessary  com- 
putations were  made  by  the  great  French  geometer  Clai- 
BAinr,7^M>  essigned  April  13th,  1769,  as  the  day  on  which 
the  «ii|M»t  would  pass  its  perihelion.      This    prediction 
watt  ;^||ipai|cri>1y  (MHTect.     The  oomet  was  fint  j«en  on 
Cb^iil)^M-4ay,    1768,  and  passed  its  perihelion^  Maroh* 
1  Jtht  1769,  iXiij  one  month  before  the  piedioted  .tune. 
'£^e  eonaiBt  wtiurQed  again  in  1836,  within  three  dikys  of 
ttie  moment  ]^»dioted  by  Dk  Poircfioooi^inr,  the  most 
suooeMfnl  ealeohtor.    The  next  return  will  iHt>babfy  take 


the  sun 
fore  pre 
1768.    B 
error,  o 


898 


AHTRONOMY. 


place  ill  ton  or  tl»I2,  tlio  exact  tiiiio  being  »til^  unknown, 

because  the  neceasary  coinputatiuius  have  noi  >et  been 

made. 
We  give  a  figure  nhowing  the  position  of  the  orbit  of 

Hallkt's  c(nuet  relative  to  the  orbits  of  tlio  four  outer 

planH.s.  It  attain- 
ed itib  greatest  dis- 
t8iK<e  from  the  snii, 
ftu'  '/eyond  the  or- 
bit of  Neptune, 
4i)Hnittheyearl878, 
and    then    oom- 

Jeikced  its  return 
<Hnt^.  Thefig- 
lire  «li0WB  the  prob- 
able pJDsitioii  of  the 
onii^t  in  1874.  It 
wrilf'ihen  far  be- 
jort^  the  reach  of 
thf  i»0Bt  powerful 
telesoopt),  bnt  its  distance  and  direction  ii4>nit  of  beuig 
calculated  with  so  mnoh  precision  that  a  ^osoope  oould 
be  pointed  at  it  at  any  required  moment    H?' 

We  have  already  stated  that  great  nnmbell^  of  comets, 
too  faint  to  be  seen  by  the  nakc^  eye,  ara  dii^tovered  by 
telescopes.  A  considerable  number  of  these  telescopic 
comets  have  been  found  to  be  periodic.  In  ii.>0Bt  cases, 
the  period  is  many  centuries  in  length,. so  that  tlio  comets 
have  only  been  noticed  at  a  single  virit.  Eight  or 
nine,  however,  have  been  found  to  be  of  a  period  ^  shoft 
that  they  have  been  observed  at  two  or  uiortf  n^O'^v 

We  present  a  table  of  such  of  the  periodic  e(ptt«to  as 
have  been  actually  observed  at  two  or  more  rMonis.  A 
number  of  others  are  known  to  be  periodic,  bnt  have  Xi^n 
observed  only  on  a  sii^le  viut  to  our  system. 


OP  ■A&unr's  oomr. 


>;WH«Btr  ^ii^mmmsm^mimmmsx:-- 


MtH  *mm»ummiJi^ 


400 


ASTRONOMY. 


Theory  of  Oometary  Orbits.— Tliora  is  ajproiicrtjr 

uiidentanuiiig  of  which  will 


of  all  c»r 
bit*  of  bodioa  around  the  miti,  an 

enable  tu  to  form  a  clear  idea  of  lonio  causeit  which  affect  the 
motion  of  cometa.  It  mav  bo  cxpreaMNl  in  the  following  theorem  : 
The  nuitn  dittanee  of  a  hmly  J'rom  the  *u»,  or  the  ntajor  inrit  of  the 
ellipee  in  which  it  revolves,  de|>ends  only  upon  the  velocity  of  the 
iHidy  at  a  given  distance  from  the  sun,  and  may  be  found  by  the 
formula, 


It  = 


H  r 


a  M  —  r  «" 


in  which  r  is  the  distance  from  the  sun,  «  the  velocity  with  which 
the  body  is  movinut  and  fi  a  constant  proportional  to  the  mass  of 
the  8>.n  and  depenains  on  the  units  of  time  and  length  we  adopt 

To  understand  this  fonuula,  let  us  imagine  ourselves  in  the  celes- 
tial spaces,  with  no  planets  in  our  neighborhood.  Suppose  we  have 
a  great  number  of  balls  and  shoot  them  out  with  the  same  velocity, 
but  in  different  directions,  so  that  they  will  describe  orbits  around  the 
Mun.  Then  the  bodies  will  all  describe  different  orbits,  owing  to 
the  different  directions  in  which  we  threw  them,  but  these  orbits 
will  all  possess  the  remarkable  jwoperty  of  having  equal  UMJor 
axes,  ana  therefore  equal  mean  distances  from  the  sun.  Sinoe,  by 
Kbplbr's  third  law,  the  ijerio-Jio  time  depends  only  upon  the 
mean  distance,  it  follows  thiat  ilvf  bodies  will  have  the  same  time 
of  revolution  around  the  bub.  Coasequentiy,  it  we  wait  patiently 
at  the  point  of  projection,  they  will  all  make  a  revolution  in  the 
same  time,  and  will  all  oome  back  again  at  the  same  moment,  each 
one  ooming  from  a  direction  the  opposite  of  that  in  which  it  was 
thrown. 

In  the  above  formula  the  aujor  axis  is  given  by  a  fraction,  having 
the  expression  3  ^  —  r  e*  for  itt  denominator ;  it  follows  that  it  the 

square  of  the  velocity  is  almost  equal  to  — ^,  the  Taloe  of  a  will 

become  very  S'^t,  because  the  denominator  of  the  fraction  will  be 
very  small.  11  tan  relooity  is  soeh  tiiat  9  ^  —  r  •*  is  lero,  the  cnean 
distance  will  become  inllnite.    Heaee,  in  this  ease  the  body  will 

a'  off  to  an  inflaite  distance  from  the  sun  and  never  ivtnm. 
ich  less  will  it  return  if  the  Telocitv  is  still  granter.  Such  a 
Telodty  will  make  the  value  of  a  slgebraioally  negative  and  will 
correspond  to  the  hyperbola. 

If  WW  take  one  kilometre  per  second  as  the  unit  of  velocity,  and 
the  mean  distance  of  the  eaith  ftramthecnn  as  Uw  unit  of  distanea, 
the  value  of  ^  will  be  representMl  by  the  nomber  87S,  so  that  the 

f ormuU  for  e  will  be  a  =  -—_———.    Fran  this  equation,  we  may 

eiiteulate  what  velocity  a  body  movins  around  the  son  must  bave 
at  any  {j^ven  distance  r,  in  order  thai  it  may  move  in  a  pandioUc 

ahall  vaniih. 


orbit— that  k,  that  the  denominator  of  the  fraetlon 
TUs  omidition  will  give 


1750 


At  the  diataneeof  the  earth 


OUJUHt  OF  VOMKTK 


AM 


Itcrty  of  »••  "•■- 
;  of  which  wilt 
rhich  affect  the 
)winK  theorem  : 
major  lurit  of  the 
1)  velocity  of  the 
bo  found  by  the 


•city  with  which 
1  to  the  moHit  of 
ingth  we  adopt, 
lives  in  the  celes- 
Buppow  we  have 
le  same  velocity, 
orbits  around  the 
orbits,  owing  to 
but  these  orbits 
ing  equal  major 
3  sun.  Since,  by 
I  only  upon  the 
e  the  same  time 
re  wait  patiently 
revolution  in  the 
me  moment,  each 
i  in  which  it  was 

a  fraction,  having 
bllowb  that  if  the 

ke  value  of  a  will 

le  firaction  will  be 
is  aero,  thecnean 
ise  «he  body  will 
nd  never  ivtnm. 
gfVKter.  Booh  a 
M^ve  and  will 

t  of  vehicity,  and 
BOiitof  diataaee, 
■  875,  M  that  the 

equation,  we  nuqr 

le  nin  must  bsve 
oive  in  ajMrabolio 
tloB  shall  vMiieh. 

itaaoe  of  tlie  earth 


from  the  sun  we  have  r  =  1,  so  that,  at  that  diHtancc,  t  will  h<  tli<> 
M|uare  root  of  17S0,  or  nearly  43  kilometres  |H)r  Mccond.  The  fur 
ther  we  K*'t  out  from  the  huh,  the  Icmm  it  will  )h!  ;  and  we  may  remark, 
H8  an  interesting  theorem,  that  whenever  the  eomet  is  at  the  dis- 
tance of  one  of  the  planetary  orbits,  its  velocity  must  Imi  c(|unl  ti> 
that  of  the  iilanet  multiplied  by  the  square  root  of  2,  or  1-414,  etc. 
Hence,  if  the  velocity  of  any  planet  were  suddenly  incream>d  by  a 
little  more  than  -,%  ot  its  amount,  its  orbit  would  lie  changed  into 
a  paralM>la,  and  it  would  flv  away  from  the  Hun,  never  to  return. 

It  follows  from  all  this  that  if  the  astronomer,  by  observing  the 
course  of  a  comet  along  its  orbit,  can  determine  its  exact  velocity 
from  point  to  point,  he  can  thence  calculate  its  mean  distance  from 
the  sun  and  its  periodic  time.  But  it  is  found  that  the  velocity  of 
a  large  majority  of  comets  is  ho  nearly  equal  to  that  required  for 
motion  in  a  parabola,  that  the  difference  eludes  oliservation.  It  is 
hence  concluded  that  most  comets  move  nearly  in  parabolas,  and 
will  either  never  return  at  all  or,  at  best,  not  until  after  the  laiiseof 
many  centuries. 

$;  6.  omonr  or  ocmmn. 

All  that  wo  know  of  comets  leems  to  indicate  that  tbey 
did  not  originally  belong  to  oor  system,  bnt  became  mem- 
liera  of  it  through  the  tKitovbing  forces  of  the  planets. 
From  what  was  said  in  tin  bit  SMtion,  it  wid  be  seen  tiiat 
if  a  comet  is  moving  in  a  pandxdie  (nrbit,  and  its  vdooUy 
is  diminished  at  any  point  by  ever  so  small  an  amount,  ite 
orbit  will  be  changed  into  an  "tUipse  ;  for  in  order  that  the 
orbit  may  be  parabolic,  the  quantity  2  /*— r  v'  most  remain 
exactly  zero.  Bnt  if  we  then  diminish  v  by  the  smallest 
amount,  this  expression  will  become  finite  and  positive, 
and  a  will  no  longer  be  infinite.  Now,  the  attraction  of 
a  phmet  may  have  either  of  two  opposite  effects ;  it  may 
eidier  increase  or  diminish  the  velocity  of  the  c<miet. 
Hence  if  Haa  latter  be  moving  in  a  parabolic  orbit,  the  at- 
traotioit  ef  a  phmet  mi^^t  either  thh>w  it  out  into  a  hyper- 
bolic orbit,  so  tlMt  it  would  never  again  return  to  the  sun, 
but  wander  irnvrw  through  the  celestial  spaoee,  or  it 
might  change  its  ortrit  into  a  more  or  less  elongated  ellipse. 

Suppoie  CJ^  to  represent  a  small  portion  of  the  cnbit 
of  the  planet  aitd  AB%  small  poHion  of  the  orbit  of  a 
comet  passlBg  near  it.    Suppose  -also  that-the  eomet  passes 


ASTItOHOMY. 


a  little  in  fnmt  <>f  the  plniiot,  and  that  the  alinultanenuii 
{HMitiuiiH  of  the  two  bodied  are  ropn»oiit«<l  hy  the  conre- 
apondiiig  lottore  of  the  alplmlHjt,  a,  A,  o,  </,  etc. ;  tlie  aliortoat 
distance  of  the  two  botlie*  will  Imj  the  line  o  c,  and  it  is 
then  that  the  attraction  will  be  the  most  jioworful. 
between  o  v  and  d  d  the  planet  will  attract  the  comet  ahno«t 
directly  Uckward.  It  follows  then  that  if  a  comet  p»«8 
the  planet  in  the  way  hero  represented,  its  velocity  will  be 
retarded  by  the  attraction  of  the  latter.  If  therefore  it  be 
a  parabolic  comet,  tlie  orbit  will  be  changed  into  an 
ellipse.  The  nearer  it  passes  to  the  pUmet,  the  greater 
will  be  the  change,  so  long  as  it  passes  in  front  of  it.     If 

it  passes  belund,  the 
reverse     effect    will 
follow,  and  the  mo- 
tion will  be  aocele* 
rated.    The  orbit  will 
then  be  changed  into 
a  hyperbola.    The  or- 
bit finally  described 
after  the  oomet  leaves 
|onr  ■ystem  will  de- 
ind  npon   whether 
its  velodty  is  aooele- 
rated  or  retarded  by 
tile  oombined  attrMstion  of  all  the  planets. 

All  the  studies  which  have  been  made  of  comets  seem 
to  show  that  they  originally  moved  in  pMraboliooibita,  and 
were  brought  into  elliptic  orbits  in  this  way  by  the  attvao' 
tion  of  some  planet.  The  planet  which  has  thus  hronght 
in  the  greatest  number  is  no  doubt  JttpUar.  In  fact,  the 
orbits  of  several  of  the  periodic  comets  peas  very  near  to 
that  phmet.  It  mi^t  seem  that  these  oHbits  oii|^t  dmoat 
tointmectthatof  thephu)etwhididumgedth«n.  Thia 
would  be  true  at  first,  but  owing  to  the  constant  diange  in 
the  position  of  the  oometary  cn^it,  produced  by  the  at* 
traction  oi  the  plaiMits,  the  orbits  would  gradndly  mo^ 


108.— AmuonoH  or  ruurarr  ok 

OOMMT. 


M^ 


iuMWiiii>Mi>.it8iiy'i.niiwwwi 


wamm 


ORUUN  OF  VOMKIK 


4U3 


siinnltancouR 
»y  tlio  corre- 
;  thuBliortost 
0  0,  aiid  it  is 
»t   iwworful. 
couiot  abiiuHt 
a  cuiiiut  p»M 
looity  will  be 
liereforo  it  be 
tgud  into  ail 
t,  the  greater 
ont  of  it.     If 
8  behind,  the 
effect    will 
and  tlie  mo- 
ill  be  aooele- 
Tlio  orbit  will 
)  changed  into 
•bola.   The  or- 
ally described 
le  oomet  leaves 
item  will  de- 
ipon   whether 
M)it/  is  acoele- 
>r  retarded  by 

comets  seem 

olio  ortiita,  and 

by  the  altnus- 

B  tbns  bronght 

In  fact,  the 

IS  very  near  to 

oQl^t  almost 
dthem.  This 
itant  change  in 
oed  by  the  ai- 
pradwdly  move 


away  from  oach  other,  tH>  that  in  time  there  might  be  no 
approach  whatever  of  the  pUnet  to  the  comet. 

A  rumarkabh  case  of  this  sort  was  afforded  by  a  comet 
()i»cuvored  m  Jtme,  1770.  It  wan  obsorvud  in  all  nearly 
four  months,  and  was  for  some  time  visible  to  the  naked 
uyu.  On  calculating  its  orbit  from  all  the  oliservations, 
the  astronomers  were  astonished  to  find  it  to  be  an  ellipse 
with  a  |)eriod  of  only  five  or  six  years.  It  ought  dieref  ore 
tu  have  appeared  again  in  1776  or  1777,  and  should  have 
rutnmed  to  its  perihelion  twenty  times  before  now,  and 
should  also  have  been  visible  at  returns  previonsto  that  at 
which  it  was  first  seen.  But  not  only  was  it  never  seen 
before,  but  it  has  never  been  seen  since  I  The  reason  of 
its  disappearance  from  view  was  bronght  to  light  on  cal- 
culating its  motions  after  its  flrat  discovery.  At  its  re- 
turn in  1770,  the  earth  was  not  in  the  right  part  of  its 
orbit  for  seeing  it.  On  passing  ont  to  it*  aphelion  again, 
about  the  beginning  of  1779,  it  oneounterad  the  planet 
Jwjnter,  and  approached  so  near  it  that  it  was  impoauble 
to  determine  on  which  side  it  passed.  This  approach,  it 
will  be  remembered,  wold  not  be  observed,  beoanse  the 
comet  wa*  entirely  ont  of  sight,  bntH  was  calenlated  with 
absolute  certainty  from  the  theoiy  of  the  comet's  motion. 
The  attraction  of  JitpUetf  therefore,  threw  it  into  aom» 
orbit  so  entirely  different  that  it  has  never  bMn  seen  since. 

It  is  abo  hi|^y  ptobable  that  the  oomet  had  jnst  been 
brought  in  hj  the  attraetion  of  Jitter  on  the  rery  revo- 
lution  in  which  it  was  first  observed.  Its  history  is  this : 
ApproMhing  the  son  fmn  the  steUar  spaces,  probably  for 
the  first  time,  it  passed  so  near  Jupiter  In  1767  that  its  or- 
bit was  flliangBd  to  an  eOipae  of  abort  period.  It  noade 
two  complete  revolutions  around  the  sun,  and  in  1779 
again  mat  the  planet  near  the  same  phuse  it  had  met  him 
iiefore.  The  orMt  was  again  ahwed  so  mnoh  that  no  tel- 
eaoope  Yum  fonnd  the  oomet  ainee.  No  other  case  so  re- 
markaUe  as  this  ha*  evnr  been  noticed. 

Not  <«ly  are  new  oometa  oeearionaUy  brought  in  from 


y 


SI- 


404 


ASTRONOMY. 


m. 


#'  i 


the  stellar  spaces,  but  old  ones  may,  as  it  were,  fade  away 
and  die.  A  case  of  this  sort  is  afforded  by  Biela's  comet, 
which  has  not  been  seen  since  1S52,  and  seems  to  have  en- 
tirely disappeared  from  the  heavens.  Its  history  is  so  in 
structive  that  we  present  a  brief  synopsis  of  it.  It  was  first 
observed  in  1772,  again  in  1805,  and  then  a  third  time  in 
1836.  It  was  not  until  this  third  apparition  that  its  peri- 
odicity was  recognized  and  its  previous  appearances  iden- 
tified as  those  of  the  same  body.  The  perioil  of  revolu- 
tion was  found  to  bo  between  six  uid  seven  years.  It  was 
BO  small  as  to  be  visible  in  ordinary  telescopes  only  when 
the  earth  was  near  it,  which  would  occur  only  at  one  re- 
turn out  of  three  or  four.  So  it  was  not  seen  again  until 
near  the  end  of  1845.  Nothing  remarkable  was  noticed  in 
its  appearance  nntil  January,  1846,  when  all  were  aston- 
ished to  find  it  separated  into  two  c<.mplete  comets,  one  a 
little  brighter  than  the  other.  The  computation  of  Pro- 
fessor MiTBBABD  makes  the  distance  of  the  two  bodies  to 
have  been  200,000  mWes. 

The  next  observed  rotnm  was  that  of  1852,  when  the 
two  comets  were  again  viewed,  but  far  more  widely 
separated,  their  distance  having  increased  to  about  a  mil- 
lion and  a  half  of  miles.  Their  brightnetn  was  so  nearly 
equal  that  it  was  not  poerible  to  dedde  which  should  be 
considered  the  principal  comet,  nor  to  determine  with 
certainly  which  one  should  be  oonsidered  aiB  identical  with 
the  comet  seen  during  the  jo^vious  apparition. 

Thoni^  carefully  looked  for  at  every  subsequent  return, 
neidier  oomet  hasbem  fieen  since.  In  1872,  Ur.  Poosoir, 
of  Madras,  thought  that  he  got  a  monMataryiview  of  the 
comet  tiirongh  an  opening  l«tween  the  dondson  a  stormy 
evening,  but  the  position  in  which  he  rappoied  himself  to 
observe  it  was  so  far  from  the  oahmlated  (hm  that'his  obser- 
vation has  not  been  aoeepted. 

Instead  of  the  cornet^  however,  wo  had  a  meteorio  i^Miwer. 
The  orbit  of  tiiis  comet  almoBt  interseots  that  ni  tlie  enrtii. 
It  was  therefo««  to  be  <»pected  that  the  latter,  OH  passing 


REMARKABLE  COMETS. 


406 


ero,  fade  away 
Mela's  comet, 
ms  to  have  en- 
listory  i8  so  in 
It  was  first 
\  third  time  in 
1  that  its  pcri- 
tearances  iden- 
o\  of  revolu- 
yeans.  It  was 
pes  only  when 
>nly  at  one  re- 
en  again  until 
was  noticed  in 
Jl  were  aston- 
I  comets,  one  a 
itation  of  Pro- 
two  bodies  to 

852,  when  the 
more  widely 
to  abont  a  mil- 
I  was  so  nearly 
lioh  should  be 
etermine  with 
I  identical  with 
loo. 

leqnent  return, 
I,  Mr.  Poofloir, 
ry<Tiew  of  the 
ids  on  a  stormy 
used  himself  to 
that'his  obMr- 

steocio  idioiwer. 
It  of  tibs  earth, 
ter,  oiipMMing 


the  orbit  of  the  comet,  would  intersect  tlie  fragmentary 
meteoroids  supposed  to  follow  it,  as  explained  in  the  last 
chapter.  According  to  the  calculated  orbit  of  the  comet,  it 
crossetl  the  point  of  intersection  in  September,  1872,  while 
the  earth  passes  the  same  point  on  November  27th  of  each 
year.  It  was  therefore  predicted  that  a  meteoric  shower 
would  be  seen  on  the  night  of  November  27th,  the  radiant 
point  of  which  would  be  in  the  constellation  Andromeda. 
This  prediction  was  completely  verified,  but  the  meteors 
were  so  faint  tiiat  though  they  succeeded  each  other  quite 
rapidly,  they  might  not  have  been  noticed  by  a  casual 
observer.  They  all  radiated  from  the  predicted  point  witli 
such  exactness  iiiat  the  eye  could  detect  no  deviation  what- 
ever. 

We  thus  have  a  third  case  in  which  meteoric  showers 
are  associated  with  the  orbit  of  a  oomet  In  this  case,  how- 
ever, the  comet  has  been  completely  dissipated,  and  proba- 
bly has  disappeared  forever  from  telescopic  vidon,  tliough 
it  may  be  expected  that  from  time  to  time  its  invirible 
fragments  will  form  meteors  in  the  earth's  ^mosphero. 

ft  6.    BJDMABXABLB  OQHXM. 

It  is  &miliarly  known  that  bright  comets  were  in  former 
yecjs  objects  of  great  terror,  being  supposed  to  prewge 
the  fall  of  empires,  the  death  of  monarch*,  tiie  vpfHimAi 
of  earthqnakM,  wan,,  peatilenoe,  and  eveiy  otho*  odamity 
which  eoold  affliet  mankind.  In  showing  the  entire 
gronndleasnea  of  loeh  fean,  soimoe  has  rendered  one  of  its 
graptert  benefit*  to  mankind. 

bi  1456,  the  oomflt  known  as  Hallkt's,  appearing 
when  tihe  TnrkiirMW  making  war  onCShrisfeoidom,  censed 
snoh  terrw  that  Pc|ie  OxuxTva.  wrdend  pnqrers  to  be 
oierod  in  the  Indies  for  praleetion  againit  it.  TW* 
is  BUiqpoasd  to  be  the  origin  of  the  popohr  myth  that  tike 
P(me  oooe  imwd  a  ball  agiinsi  the  oomet 

The  nnmber  of  comets  visible  to  the  naked  eye,  so  far  as 


■N 


406 


ASTRONOMY. 


recorded,  has  generally  ranged  from  20  to  40  in  a  cen- 
tury. Only  a  small  portion  of  these,  however,  have  been 
BO  bright  as  to  excite  nniversal  notice. 

Oomat  of  1880. — One  of  the  most  remarkable  of  these 
brilliant  comets  is  that  of  1680.  It  inspired  sach  terror 
that  a  medal,  of  wlueh  we  ]»<eseBt  a  fignre,  was  struck 
npon  tiie  Oontineiit  of  ]&m>pe toqui^ a^«hei»i<m.  A 
free  tiwidatkm  of  the  insoription  is :  "  T^  star  thveetens 
evil  things ;  trost  «dy  I  God  will  torn  them  to  good:*' 
What  makes  this  wnxA  espeoiaUy  rraiarinUe  in  histcwy 
is  that  NswTOH  oaloalated  its  orUt,  and  diowed  that  it 
moved  around  the  sun  in  a  conic  section,  in  obedience  to 
the  law  of  gravitation. 


eeMR  o«  i«M. 


Otaet  OiMMt  of  1811.  -.1%.  119  alttim  ili  geneml  ap- 
peaiwoe.  It  has  a  period  of  oivier  MOO  yean,  and  its 
a^fBliQB^iiCai|O0i8abeat4O^OOQ»O9O,O<N>^iiiaM.     . 

QKm:^mm  of  lS48..--Oiie  of  l^mat  hOXmA  mm- 
ets  whidi  kmmappoarad  dnfibg;^  priaiml  .owilwy-iww 
tha^  of  fefani^^lMS.  It  v»  viaSbfe  Jn  irii  4MiMit 
oIoBeto.tbeMui.    Oonaldenlile  tuwor  into«««^ri  fe^Moe 

whuhJiidlMfln  peMkled  lor  thai  yew  ^^mUm,:  Ai 
periiielitiii  it  pooied  neafer  the  son  than  Miy  oiker  body 
has  ever  been  known  to  pass,  the  kMt  diilaMe  bdng  only 
abont  one  filth  <rf  Ike  nm's  seni-dlameler.  WA  « tMy 
eiight  ohange  of  its  original  motkU)  itwotid  kave  astMlly 
Men  into  the  son. 


40  in  a  cen- 
mr,  Lave  been 

kable  of  these 
k1  sach  terror 
re,.WMstniek 
dwnikm.  A 
BtartlnmitenB 
urn  to  goodi" 
lUe  in  hiskwy 
bowed  that  it 
I  obedienee  to 


mim. 
i»igmiml§!p. 

nwVt  ■ 


Jdi4i^t 


GREAT  COMET  OF  1868. 


407 


0(Mt  OooMl  of  18B8. — ^Another  remarkable  comet  for 
the  length  of  time  it  ranained -viable  was  that  of  1868. 
It  is  f reqnentlj  oallad  after  th«  nsme  of  DosAn,  its  iin»t 
diMMMrerar.     Mo  oamet   Hik&ni^  ov  Mighboriiood  in 


wiuiswteiyUftiftpw 


the  ob«0nratioiMnia(b  ttpovithftve  already  been  preaented! 


flu.  lll.-HpaMA«'t  MMIf  m 


mm 


iii»0ltl^i^mmmmAV'.ms-:M.'m%tfM-A''-'  ■  -^^:^-:-'r 


HWlllUiailli..i'/Hl.imilil 


ENOKtrS  COMET. 

Its  greatest  brillianoy  oecnrred  about  the  beginning  of 
October,  when  its  tail  was  iO*  in  length  and  10°  in  breadth 
at  its  outer  end. 

DoHATi'g  omnet  had  not  l<Hig  been  obaenred  when  it 
was  found  that  ita  orbit  was  deddedljr  elliptioal.  After  it 
disappeared,  the  observatioiia  were  all  earefnlljr  investigaiad 
by  two  Biathematidansy  Dr.  Yov  Asm,  of  Oermaay, 
and  Mr.  O.  !¥.  Uttx,  of  this  eoontry.  The  hitter  found 
a  period  of  1960  yean,  whieh  is  probably  within  a  half  a 
oentnrjr  of  the  truth.  I|  is  probable,  therefora,  that  this 
comet  appeared  about  the  ilrst  eentuiy  before  the  Chris- 
tian era,  and  will  rrtum  again  about  the  year  8800. 


tioa^ 


kaowa  MrlMp's  eontt    h»  fuMi  kt  Wfmm  Hkm  mtA  four 

1^  MSiiii»at^t»Mr  aast  o«e  smST  ^iS«  the  msI  fH«% 

°'gi^'*i''^^J!/g*^*'^  *°  »*  ""^  n^  TlwdwwMlaaflt 
*^  ^^^  ^ '■'^  *>*''>*^  *<>  *^  «(«Mt  ii  tlM  tiM  obMmiloat 
wUab  kave  tepi  aude  Upoa  It  mmi  to  iwll«t|s  tkat  it  to  gnms^ 
amoMttilgiksnB.  BtwaB  attrfboted  tUs  diai^  ia  ila  ocSSig 
tM>MMMM^«Ma«l  ireriitt^ 

VMa^r  M«*wto  Mim  lftto^fariad^^ 
lO*  «om*wM  asiaallr  «nK4tlM  MB. 

>ai HMr .ynioa  of  'BMip *s  (OoiBtt  awMt  bs  dHi% 

iSiySJWi^  *W»^  MBlst  MiMii'  iMMnNr  the  Mtt'lhatf  aM» 

52f i2'-*2S ISSSf^iLf*  ««I««w»» to isttls.  Wfiiol to 
«w  ay  <w<>ii|  ilWIIIi  Mjit  aaoiatftos  fat  ttidr  awtioaa  wlMnra- 

tdntf  «ha|  «•  di^idrftom  Ohm  of  UwplsS!. 


fe  MPA'llil^lW''ti'*V'-^W«WW WW^^  ^%sm»Wiw<iiH«ii»)g|iiJa!!MiwMMM'  aaW!MaiUii.i! 


PART   III. 

THE    UNIVERSE  AT  URGE. 


INTRODUCTION. 

Ik  onr  stndies  of  the  lieavenly  bodies,  we  have  hitherto 
been  occupied  almoet  entirely  with  those  of  the  solar  sys- 
tem. Although  this  system  comprises  the  bodies  which 
are  most  important  to  us,  yet  they  form  only  an  insignifi- 
cant part  of  creation.  Besides  the  earth  on  which  we 
dwell,  only  seven  of  the  bodies  of  the  solar  system  are 
plainly  visible  to  the  naked  eye,  whereas  it  is  well  jjpwni 
that  8000  Stan  or  more  can  be  seen  on  any  clear  ^^t 
We  now  have  to  describe  the  visible  universe  in  its  hugest 
extent,  and  in  doing  so  shall,  in  imagination,  step  over 
the  bounds  in  which  we  have  hitherto  confined  onnelvM 
and  fiy  through  the  immensity  of  space. 

The  material  univene,  as  revealed  by  modem  telescopic 
investigation,  consists  principally  of  shining  bodies,  many 
milHona  in  number,  a  few  of  the  nearest  and  brightest  of 
which  ap«  visible  to  the  naked  eye  as  stars.  They  extend 
ontas&raathe  moa*:  powerful  telescope  can  penetrate, 
and  no  4|w  knows  how  much  &rther.  Our  sun  is  simply 
one  of  then  stan,  and  does  not,  so  far  as  we  know,  differ 
from  its  f^rws  in  any  esMiitial  oharaeteristic.  Frran  ihe 
most  caraM  estimates,  it  is  rather  less  bri^t  than  the 
avcfige  «^|he  nearer  stars,  and  overpowen  them  by  its 
briOiaiMgr  ^ty  because  it  is  so  much  nearer  to  us. 
Tbe  i^anoe  of  the  stan  from  each  other,  and  th««fore 


412 


A8TH0N0MT. 


from  the  sun,  is  immenflely  greater  than  any  of  the  dis- 
tiuicu8  which  we  have  hitherto  had  to  consider  in  the  Bolar 
system.  Suppose,  for  instance,  that  a  walker  through 
the  celestial  spaces  could  start  out  from  the  sun,  taking  steps 
8000  miles  long,  or  equal  to  the  distance  from  Liverpool  to 
New  York,  and  making  120  steps  a  minute.  This  speed 
would  carry  him  around  the  earth  in  about  four  seconds ; 
he  would  walk  from  the  sun  to  the  earth  in  four  hours,  and 
in  five  days  he  would  reach  the  orbit  of  Neptiu,ne.  Yet  if 
he  should  start  for  the  nearest  star,  he  would  not  reach  it 
in  a  hundred  years.  Long  before  he  got  there,  the  whole 
orbit  of  N«]^iwMy  supposing  it  a  visible  object,  would 
Ihiave  been  raduced  to  a  point,  and  finally  vanish  from 
sight  altogether.  In  fact,  the  nearest  known  star  is  about 
seven  thousand  times  as  f ar  aa  the  planet  NepUkM,  If 
we  suppose  the  orbit  of  this  planet  to  he  represented  by  a 
child's  hoop,  the  nearest  star  would  be  three  or  four  miles 
away.  We  have  no  reason  to  suppose  that  oontignons 
stMSl  ire,  on  the  average,  nearer  than  this,  ezoept  in  special 
eMi|l^  where  they  are  oolleoted  together  in  olnsters. 

9^  total  number  of  the  stars  is  estimated  by  millions, 
and  they  are  probably  separated  by  theM  wide  intervals. 
It  loUowB  that,  in  going  from  the  sun  to  the  nearest  star, 
;J|i»  wonld  be  simply  taking  one  step  in  the  universe.  The 
most  distant  stars  visible  in  great  tdesoopes  are  probably 
sevovl  thousand  times  more  distant  than  the  nearest  one, 
and  we  do  not  know  what  may  lie  beyond. 

The  point  we  wish  prindpdUy  to  impress  on  the  foftder 
in  this  connection  is  that,  although  the  stan  and  plan^  px«- 
sent  to  the  naked  eye  so  great  a  similarity  in  appearance, 
there  is  the  greatest  possible  divenity  in  their  distances 
and  characters.  The  planets,  though  many  millions  of 
miles  away,  are  comparatively  near  as,  and  fcurm  a  little 
family  by  themselves,  which  ii  oalled  the  soihr  lyatem. 
The  fixed  stars  are  at  distances  inmm^parably  yeatair  the 
nearest  star,  aa  jnst  stated,  beii^  thoiuands  of  timaatnore 
distant  than  the  farthest  phuiet    The  phmets  we,  ao  far 


i.,,Tl»ijl,HM-W  l-'J-!^ 


,^,,uii|im 


»!f  HI**'.  iflmsv'ST-S  '•• 


THE  UNIVBR8K  AT  LA  ROB. 


118 


than  any  of  the  du- 

consider  in  the  solar 
i  a  walker  through 
1  the  sun,  taking  steps 
oe  from  Lirerpool  to 
ninnte.     This  speed 

about  four  seconds ; 
th  in  four  hours,  and 
of  Neptrune.  Yet  if 
9  wonld  not  reach  it 
got  there,  the  whole 
sible  objeet,  wonld 
finally  vanish  from 

known  star  is  about 
lanet  Neptune,     If 
be  represented  by  a 
)  three  or  four  miles 
ose  that  contig^oos 
ilia,  exeept  in  special 
■  in  clusters, 
imated  by  millions, 
leMwide  intervals. 
I  to  the  nearest  star, 
the  universe^     The 
oopes  are  probably 
an  the  nearest  (me, 
>nd. 

press  on  the  iMder 
twn  and  planets  ]Hre- 
rity  in  appeavaaoe, 
'in  tlmr  distanoes 

naany  niilli<Hu  of 
,  aad  form  a  little 
1  the  solar  lyatom. 
nably  |^«at«r-4he 
mds  of  tiaMi  titafe 
pknelB  aie,  ao  f«r 


as  we  can  see,  worlds  somewhat  like  this  en  which  we  live, 
wliile  the  stars  are  suns,  generally  larger  and  brighter  than 
our  own.  Each  star  may,  for  aught  we  know,  have  plan- 
ets revolving  around  it,  but  their  distance  is  so  immense 
that  the  largest  planets  will  reuuun  invisible  with  the  most 
powerful  telescopes  man  can  ever  hope  to  construct. 

The  clasrification  of  the  heavenly  bodies  thus  leads  us  to 
this  curious  conclusion.  Our  sun  is  one  of  the  family  of 
stars,  the  other  members  ol  whidi  stud  the  heavens  at 
night,  or,  in  other  words,  the  stars  are  suns  like  that  which 
makes  the  day.  The  planets,  though  they  look  like  stars, 
are  not  such,  but  bodies  more  l^e  the  earth  on  which 

we  live. 

The  great  universe  of  stars,  including  the  creation  in  its 
largest  extent,  is  called  the  ateUar  «y«feti»,  or  tieUa/r 
uniiferte.  We  have  first  to  oonnder  how  it  looks  to  the 
naked  eye. 


■^ 


CHAPTER  I. 


THE  CONSTELLATIONS. 


/ 


g  1.  ammajLL  asfbot  of  thb  HBAnmi. 

When  we  view  the  heavens  with  the  unasHisted  eye,  the 
Btara  appear  to  be  scattered  nearly  at  random  over  Uie 
fiurfaoe  of  tlie  celestial  vault.  The  only  deviation  from  an 
entirely  random  distribution  which  can  be  noticed  is  a  cer- 
tain grouping  of  the  brighter  ones  into  constellations. 
We  notice  also  that  a  few  are  comparatively  much  bri^ter 
than  the  rest,  and  that  there  is  every  gradation  of  bril- 
liancy, from  that  of  the  brightest  to  those  which  are  barely 
visible.  We  also  notice  at  a  glance  that  the  fainter  stars 
outnumber  the  bright  ones ;  so  tluit  if  we  divide  the  stars 
into  classes  according  to  their  brilliancy,  the  fainter  classes 
will  be  far  the  more  numerous. 

Tlie  total  number  one  can  see  will  depmd  very  lai^ly 
upon  the  clearness  of  the  atmosphere  and  the  keenness  of 
the  eye.  From  the  most  careful  estimates  whidi  have 
been  made,  it  would  appear  that  there  are  in  the  whole 
celestial  sphere  about  6000  stars  visible  to  an  <M!dinarily 
good  eye.  Of  these,  however,  we  can  never  see  more  than 
a  fraction  at  any  one  time,  be<»U8e  one  half  of  the  sphere  is 
always  of  necessity  below  the  horizon.  If  we  could  see  a 
star  in  the  horizon  as  well  as  in  the  zenith,  one  half  of  the 
whole  number,  or  8000,  would  be  visible  on  any  dear  night. 
But  stare  near  the  horizon  are  seen  through  so  grMt  a 
thickness  of  atmosphere  as  greatly  to  obscure  their  light ; 
consequently  only  the  brightest  ones  can  there  be  seen.  As 


CLASaSa  OF  Hl'AHH. 


415 


S. 


/ 


lasHiBted  eye,  the 
andoin  over  tlie 
eviation  from  an 
I  noticed  is  a  oer- 
0  confltellations. 
ly  much  bri^ter 
nidation  of  bril- 
which  are  barely 
the  fainter  stars 
\  divide  the  stars 
he  fainter  ohuwes 

end  v«ry  lai^ly 
the  keenness  of 
ites  whidi  have 
LTB  in  the  whole 
to  an  <M!dinarily 
rer  see  more  than 
f  of  the  sphere  is 
f  vre  ooidd  see  a 
I,  one  half  of  the 
lanydearnight. 
rough  so  gfMt  a 
sore  their  light; 
lere  be  seen.  As 


a  result  of  this  obscuration,  it  is  not  likely  that  more  than 
2()00  Stan  can  ever  be  taken  in  at  a  single  view  by  any 
ordinary  eye.  About  2000  other  stars  are  so  near  the 
South  Pole  that  they  never  rise  in  our  latitudes.  Hence 
out  of  the  6000  supposed  to  be  visible,  only  4000  ever 
come  within  the  range  of  our  vision,  unless  we  make  a 
journey  toward  the  equator. 

The  Oalazy.— Another  feature  of  the  heavens,  which  is 
less  striking  than  the  stars,  but  has  been  noticed  from 
the  earliest  times,  is  the  Oalmyy  or  MUky  Way.  This 
object  consists  of  a  magnificent  stream  or  Iielt  of  white 
milky  light  10*  or  16"  in  breadth,  extending  obliquely 
around  the  celestial  sphere.  During  the  spring  mouths,  it 
nearly  coincides  with  our  horizon  in  tlie  early  evening, 
but  it  can  readily  bo  seen  at  all  other  times  of  the  year 
spanning  the  heavens  like  an  arch.  It  is  for  a  portion  of 
its  length  split  longitudinally  into  two  parts,  which  remain 
separate  throng  many  degrees,  and  are  finally  united 
a^n.  The  student  will  obtain  a  better  idea  of  it  by 
actual  examination  than  from  any  description.  He  will 
see  that  its  irregularities  of  form  and  lustre  are  such  that 
in  some  phces  it  looks  like  a  nuss  of  brilliant  clouds.  In 
the  aonthem  hemisphere  there  are  vacant  spaces  in  it 
which  the  navigates  call  coal-sacks.  In  one  of  these, 
5°  by  18%  there  is  soaroely  a  sini^  star  visible  to  the 
naked  eye  (see  Figs.  191  and  183). 

Luold  tad  TslMNwpto  Mum.  —  When  we  view  the 
heavflu  with  a  teksoope,  we  find  that  there  are  innumer- 
able Stan  too  small  to  be  seen  by  the  naked  eye.  We 
may  therefwe  divide  the  stars,  with  respect  to  brightness, 
into  two  great  wlasswi. 

Looid  Man  are  those  whidi  are  visible  vithout  a  tele- 
scope. 

TMMOopio  Sins  are  those  which  are  not  m  visible. 

When  Gaulbo  first  directed  his  telescope  to  the  heav- 
ens, about  the  year  1610,  he  perceived  that  the  Hil^ 
Way  was  composed  of  stars  too  faint  to  be  individually 


MHM 


41(1 


A8rnoNoMr. 


■oon  hy  the  unaidud  oyv.  We  tliiM  have  the  iiitoresting 
fact  that  although  tolowopic  Htam  cannot  Ikj  seen  one  by 
one,  yet  in  tho  region  of  the  Milky  Way  they  are  ho  numor- 
oua  that  they  aliine  in  inaiiBOH  like  brilliant  clouds.  IIuy- 
OHBMH  in  1056  reaolvfxl  a  largo  portion  of  the  Galaxy  into 
■tars,  and  condndod  that  it  was  compofled  entirely  of  thoni. 
Kki'lkh  congiderod  it  to  bo  a  vast  ring  of  Btars  sarronnd- 
ing  the  solar  systeni,  and  remarked  that  the  sun  most  bo 
situated  near  the  centre  of  the  ring.  Tliis  view  agrees 
very  well  with  the  one  now  received,  only  that  the  stan 
which  form  the  Milky  Way,  instead  of  lying  around  the 
solar  system,  are  at  a  distance  so  vast  as  to  elude  all  our 
powers  of  calculation. 

Such  are  iii  brief  tlie  more  salient  phenomena  which 
are  presented  to  an  observer  of  the  starry  heavens.  We 
sliall  now  ooDisider  how  these  phenomena  have  been  olas- 
sitied  by  an  arrangemont  of  the  stars  aocording  to  their 
brilliancy  and  their  situation. 

S  a.  KAOiriTUDiB  or  ths  stabb. 

In  ancient  times,  the  stan  were  arbitrarily  oUssified  into 
six  orders  of  magnitude.  The  fourteen  brightest  visible  in 
our  latitude  were  derignated  asof  thetintnugnitude,  while 
those  which  were  barely  visible  to  the  naked  eye  were  said 
to  be  of  the  sixth  magrdtnde.  This  ohMofioation,  it  will 
be  noticed,  is  entirely  arbitrary,  since  there  are  no  two 
stars  which  are  absolutely  of  the  same  brOlianoy,  while  if 
all  the  stars  were  arranged  in  the  order  of  their  aotnal 
brilliancy,  we  should  find  a  reguhr  gradation  from  the 
brightest  to  the  faintest,  no  two  being  precisely  the  same. 
Therefore  the  brightest  star  of  any  one  magnitude  is 
about  of  the  same  brilliancy  with  the  faintest  one  of  the 
next  higher  magnitude.  It  depends  upon  the  judgment 
of  the  olisenrer  to  what  magnitude  a  given  star  shal)  be 
awigned  I  so  that  we  cannot  expect  an  agreement  on  ^is 
point.    The  most  recent  and  careful  division  into  magni- 


^^  j^fmrnmrnm 


■i muw.Hiii|JLi..,a,wwiiiUjii,,,i!« 


MAONlTUDKa  OK  tiTAna. 


417 


thu  intorasting 
Im)  Buun  Olio  by 
luy  uru  m  iiniiior- 
t  oluiida.  IIuY- 
the  Galaxy  into 
Diitiroly  of  tliuiii. 
'  atars  Barrouiid- 
ho  8nn  raiut  bo 
riiis  view  agroea 
ily  that  the  itan 
)ring  around  the 

to  elude  all  our 

lenomena  which 
f  heaveiu.  We 
have  been  olaa- 
Bording  to  their 


BTAB8. 

ly  obwrified  into 
^teat  visible  in 
Mgnitnde,  while 
id  eye  were  said 
ifioation,  it  will 
9re  are  no  two 
llianoy,  while  if 
of  their  actual 
ation  fimn  the 
siaely  the  mmo. 
le  magnitude  is 
itest  one  of  the 
>  the  judgm«it 
ren  atar  ahil}  be 
reement  on  ftia 
ion  into  magni- 


tiidua  has  been  made  by  IIkis,  of  Qermany,  whoso  results 
with  respect  to  nninbers  are  as  follows.  Between  tlie 
North  Pole  and  86°  south  declination,  there  are  : 

H  Stan  of  the  first  magnitude. 

48    "      «♦       second      " 
162    "      "       third        •' 
813    "      '♦       fourth      '♦ 
864     "       "       fifth 
8974    "      "       aixth 


6866  of  the  first  six  magnitudes. 

Of  these,  however,  nearly  2000  of  the  sixth  magnitude 
are  so  faint  that  they  can  be  seen  only  by  an  eye  of  extra- 
ordinary keenness. 

In  order  to  Moure  a  more  acourate  olsisiflcatioB  and  exprewion  of 
brightneH,  Han  and  others  have  divided  each  magnitude  into 
three  orders  or  ■ub-magnitudes,  making  eighteen  orders  in  all 
visible  to  the  naked  eye.  When  a  star  was  considered  as  falling  be- 
tween two  BBagnitttdes,  both  flgnres  were  written,  potting  the  mag- 
nitude to  which  the  star  most  nearly  approaohed  first  For  in- 
stance, the  faintest  stars  of  the  fourth  magnitude  were  called  4-S. 
The  next  order  below  this  would  be  the  bri^test  of  tiie  fifth 
msgnitude ;  these  were  called  9 '4.  The  stars  of  the  average  fifth 
magnitude  were  called  8  aimply.  The  fainter  ones  were  caltod  5-6, 
and  lo  on.  Iliis  notation  is  still  used  by  some  astronomers,  but 
those  who  aim  at  arsater  order  and  preewmi  exurefs  the  magni- 
tudes in  tenths.  For  instance,  the  faintest  stan  of  the  fifth  magni- 
tude they  would  call  4*6,  those  one  tenth  fainter  4-7,  and  soon 
until  they  reached  the  avaraaa  of  the  fifth  mamitode.  which 
would  be  i-O.  The  divkioa  into  tenths  of  msgaitodes  is  as  mi- 
nute a  one  as  the  ordinary  eye  is  able  to  make. 

This  method  of  desigMting  the  brilliaaey  of  a  star  on  a  scale  of 
msonitudes  Is  not  st  aU  accurate.  Several  attempts  have  been 
maae  in  receot  thaes  to  obtabi  more  aecuratc  determinations,  by 
measuring  the  light  of  the  stars.  An  instrument  with  which  this 
can  be  done  is  oalled  a  phttomttm-.  The  results  obtsiiliBd  with  the 
photometer  have  been  used  to  correct  the  scale  of  magnitudes 
and  make  it  give  a  mwe  aoenrate  expression  for  the  light  of  the 
Stan.  The.  study  of  auch  measures  shows  thst,  for  the  most  part, 
the  htighhisss  of  the  stan  incnases  in  geometrical  progressimi  ss 
the  mapiihides  vsiy  in  siiflimetioal  pro(p«ssion.  The  stan  of  one 
BMgnitade  are  geaierally  about  U  t&nea  as  bti^t  as  those  of  the 
magaitiide  next  Mow  it.    Therefore  if  wo  take  the  light  of  a  star 


|J!!1L  j' lyU.  MWULj 


418 


ASTRONOMY. 


of  the  sixth  magnitude,  which  is  just  visible  to  the  naked  eye,  as 
unity,  we  shall  nave  the  following  scale  : 


Magnitude  6th,  brightness    1 
5th,         "  24 

4th,         "  6i 

8d,  '*  16  nearly 

2d,  "  40 

Ul»t         "        100 


<t 

4i 
it 

<i 


Therefore,  according  to  these  estimates,  an  average  star  of  the 
first  magnitude  is  about  100  times  as  bright  as  one  of  the  sixth. 
There  is,  however,  a  deviation  from  this  scale  in  the  case  of  the 
brighter  magnitudes,  an  average  star  of  the  second  magnitude 
being  perhaps  three  times  as  bright  as  one  of  the  third,  and  most 
of  the  stars  of  the  first  magnituck  brij^ter  than  those  of  the  second 
in  a  yet  larger  ratio.  Indeed,  the  first  magnitude  stars  differ  so 
greatlv  in  brightness  that  we  cannot  say  how  bright  a  standard 
star  of  that  magnitude  really  is.  Bbrwu,  for  instance,  is  probably 
500  times  as  bright  as  a  rixth  magnitude  star. 

The  logarithm  of  2i  being  very  nearly  0*40,  we  can  readily  find 
how  many  stars  of  any  one  magnitude  ara  necMsary  to  make  one  of 
the  higher  magnitude  by  multiplying  the  difference  of  the  magni- 
tude by  0*40,  aira  taking  the  numoer  corresponding  to  this  logarit£m. 

This  scale  will  enabu  us  to  odculate  in  a  rough  way  the  mujni- 
tude  of  the  nnallest  stars  which  can  be  seen  with  a  telesco^  of  given 
aperture.  The  quantity  of  light  which  a  telescope  admits  is  diractly 
as  the  aquare  of  its  aperture.  Hie  amount  of  ught  emitted  by  the 
faintest  star  visible  in  it  is  therefore  inversely  as  this  Bquare.  If  we 
increase  the  aperture  50  per  cent,  we  increase  the  seeing  power  of 
our  telescope  about  one  magnitude.  More  exactly,  the  r«uo  of  in- 
crease of  aperture  is  4^  Si,  or  1 -58.  The pufrfl  of  the  eye k  probably 
equivalent  to  a  telescope  of  about  |^  of  an  inch  in  aperture ;  that 
is,  in  a  telescope  of  this  size  the  faintest  visible  star  would  be  about 
of  the  sixth  magnitude.  To  find  the  exact  magnitude  of  the 
faintest  star  visible  with  a  larger  teleaoi^e,  we  recall  that  the 
quantity  of  light  received  by  the  objective  is  prf^portional  to  the 
square  of  the  aperture.  As  just  shown,  every  time  we  multiply  the 
square  of  tiie  aperture  by  %k,  ot  the  apertare  itself  by  the  aouace 
root  of  this  quantity,  we  add  one  magnitude  to  tiie  power  of  our 
teleioope.  Therefore,  if  we  call  a*  tiie  aperture  of  a  telesoope 
which  would  just  show  a  star  one  magnitude  brighter  tiwn  the 
first  (or  tOMg.  0),  the  aperture  neoenary  to  show  aatar  of  magnltiide 
m  win  be  found  by  mltiplying  a,  by  1'58  m  timec-^tiiai  is,  it  wiU 
be  1 .58*  Ot.    Bo,  calling  a  this  aperture,  we  have : 

tf  =  !•»•  «•  =  («•  f  8.6". 

Tsking  the  logariihma  of  botb  sides  of  the  eqnatlmi,  ami  aalnf  ap- 
proKimate  nrand  numbers  whirb  are  exiiet  saoiqjh  for  tUa  purpose : 

Iag.a=:mlog.  1-58  +  log.a«  =  ^  log.SS -»■  log.  a*  »  ^  +  Iat'««- 


mmmm. 


itfiiiw^iii.w'j-' 


mmm 


NAMBa  OF  THB  BTAR8. 


419 


the  naked  eye,  u 


riy 


rerage  itarof  the 
one  of  the  sixth, 
n  the  case  of  the 
lecond  magnitude 
third,  and  most 
hoae  of  the  second 
ide  Stan  differ  so 
bright  a  standard 
tanoe,  is  probably 

can  readily  find 
ry  to  make  one  of 
Doe  of  the  magni- 
;  to  this  logarithm, 
fa  way  the  uuwni- 
kteleseopeofgnren 
admits  udiractly 
ht  emitted  by  the 
'hisBQWue.  If  we 
e  seeing  power  of 
y,  the  rano  of  in- 
Oie  eye  is  probably 
in  iqwrture;  that 
ar  would  be  about 
magnitude  of  the 
re  reeidl  that  the 
r<<portional  to  the 
w  we  multiply  the 
lelf  by  the 
the  power  of  our 
re  of  a  teloKope 
brighter  tium  the 
star  of  magnitude 
la-tiiat  is,  it  wiU 


km,  and  usmg  ap- 
hw  this  purpeas : 


Now.  M  Just  found    when  m  =  6.  a  =  VVi  =  6-4  millimetres. 
With  these  values  or  a  and  m  we  find  ; 

log.  a«  =  -  1  -800  in  fractions  of  an  laeh. 

—  —  0-887  in  fraetions  of  a  millimetre. 
Hence,  when  the  magnitude  Is  given,  and  we  wish  to  find  the  aperture : 

1<W-  «  =  5   -  1  -808  [will  give  aperture  in  inehes.] 

log.a  =  ^'  -  0-887  [will  give  aperture  in  millimetree.j 

If  the  aperture  is  given,  and  we  reqaira  the  limiting  magnitude . 

m  =  8  loir,  a  -f  8-0  [if  a  is  in  inclies.] 
m  =  6  Ing.  a  +  80  [if  a  is  in  millimetim] 

The  magnitudea  for  diflbrent  apertures  is  shown  in  the  fdlowinv 
table: 


Apntara. 

FMMfe. 

Apeitare, 

VUMIt. 

*?©• 

^-0 

Inehw. 
0-5 

"^r 

8-8 

70 

18-S 

10-5 

80 

18-5 

no 

80 

18-8 

11-4 

100 

14-0 

11-7 

11-0 

14-8 

ISO 

180 

14-4 

18-8 

150 

14-8 

18-5 

18-0 

16-8 

187 

8«0 

10- 1 

18-8 

84-0 

16-6 

8.  THB  oamna:iLA,Tzoini  akd  k 


OF  TBI 


The  earliest  artronomfflv  divided  the  8tan  into  groups, 
called  constellatiiHw,  and  fj^ye  apedai  propor  names  both 
to  these  groaps  and  to  many  of  the  more  eonsi^ononB 
stam.  We  hare  no  reo<nd  of  the  prooen  bj  which  this 
was  done,  or  of  the  eonsidarations  which  led  to  it  It  was 
long  befofe  the  oommenoement  of  history,  as  we  maj  in- 
fer fivm  dil^pent  attiwons  to  the  stan  and  oonstdlatiom 
in  the  book  of  Jnhf  which  is  supposed  to  be  among  the 


420 


A8TSON0MT. 


must  ancient  writings  now  extant.  We  have  evidence 
that  more  than  3000  years  before  the  commencement  of 
the  Christian  chronology  the  star  SiritUf  the  brightest  in 
the  heavens,  was  known  to  the  Egyptians  under  the  name 
of  Sothis.  Arcturus  is  mentioned  by  Job  himself.  The 
seven  stars  of  the  (Tr^jS^or,  so  conspicuous  in  our  north- 
ern sky,  were  known  under  that  name  to  Homeb  and  He- 
sioD,  as  well  as  the  group  of  the  Pleiades,  or  Seven  Stars, 
and  the  constellation  of  Orion.  Indeed,  it  would  seem 
that  all  the  earlier  civilized  nations,  Egyptians,  Ohinese, 
Greeks,  and  Hindoos,  had  some  arbitrary  division  of  the 
surface  of  the  heavens  into  irregular,  and  often  fontastic 
shapes,  which  were  distinguished  by  names. 

In  early  times,  the  names  of  heroes  and  animals  were 
given  to  the  constellations,  and  these  designations  have 
come  down  to  the  present  day.  E!ach  object  was  sup- 
posed to  be  painted  on  the  surface  of  the  heavens,  and  the 
stars  were  designated  by  their  position  upon  some  portion 
of  the  object.  The  ancient  and  medieval  astronomera 
would  speak  of  "the  bright  star  in  tlie  left  foot  of 
<?no»,"  "theeyeofthe^tiW,"  "theheartof  theiVf*.,  ' 
"  the  head  of  P«r«cw»,"  etc.  These  figures  are  stiu' 
tained  upon  some  star-diarts,  and  are  useful  where  >v>» 
desired  to  compare  the  older  descriptions  of  the  constelUiP 
tions  with  our  modem  maps.  Otherwise  they  have  ceased 
to  serve  any  purpose,  and  are  not  generally  found  on  maps 
designed  for  astronomical  uses. 

The  Arabians,  who  used  this  clumsy  way  of  d6a%nating 
stars,  gave  special  names  to  a  large  number  of  ^he  brighter 
ones.  Some  of  these  names  are  in  oomm<m  use  at  the 
present  time,  as  Aldebarant  FomtMatU,  etc.  A  few  other 
names  of  bri^t  stars  have  come  dovm  from  prduatoric 
times,  that  of  Ardurut  for  instance :  they  are,  1m>w- 
evw,  gradually  falling  out  of  use,  a  system  ot  ntnaaenela- 
ture  introdnoed  in  m^em  times  having  been  subttitntid. 

la  16M,  Batsb,  of  Germany,  nuq>p^  d<yim  the  ooivtd- 
lKti(»B  upon  charts,  dengnating  tiMft  brin^ter  stem  of  «ii^ 


i>aSai!iMtlMfciJi.Mftl.miKMWftl8li^^ 


NAMINO  THB  8TAR8. 


421 


have  evidence 
mencement  of 
e  brightest  in 
nder  the  name 
himself.  The 
B  in  our  north- 
OMEB  and  He- 
>r  Seven  Stars, 
it  would  seem 
tians,  Ohinese, 
livision  of  the 
often  fantastic 

animals  were 
agnations  have 
bjeot  was  snp- 
Bavens,  and  the 
a  some  portion 
'al  astronomers 
B  left  foot  of 
tof  ihe7w»  ' 
KB  are  stii 
ful  whore 
)f  the  constelia- 
ley  have  ceased 

ound  on  maps 

of  defdgnating 
of  ^he  brighter 
Hon  uae  «t  the 
AfewoUier 
'om  preluatoric 
are,  how- 
nmneaelfr- 
na  subtdtnted. 
wntheooQitil- 
Nr  iteii  of  ««dk 


hey 
of 


constellation  by  the  letters  of  the  Greek  alphabet.  When 
this  alphabet  was  exhausted,  he  introduced  the  letters  of 
the  Boman  alphabet.  In  general,  the  brightest  star  was 
designated  by  the  first  letter  of  the  alphabet  or,  the  next 
by  the  following  letter  /),  etc.  Although  this  is  sometimes 
supposed  to  have  been  his  rule,  the  Greek  letter  affords 
only  an  imperfect  clue  to  the  average  magnitude  of  a  star. 
In  a  great  many  of  the  constellations  there  are  deviations 
from  the  order,  the  brightest  star  being  /3 ;  but  where  stars 
differ  by  an  entire  magnitude  or  more,  the  fainter  ones 
nearly  dways  follow  the  brighter  ones  in  alphabetical  order. 

On  this  system,  a  star  is  designated  by  a  certain  Greek 
letter,  followed  by  the  genitive  of  the  I^tin  name  of  the 
constellation  to  which  it  belongs.  For  example,  a  Cania 
Moforis,  or,  in  English,  a  of  the  Great  Dog,  is  the  desig- 
nation of  SHritu,  the  brightest  star  in  the  heavens.  The 
seven  stars  of  the  OretU  ^dor  are  called  a  Urace  Mc^oru, 
P  UrtOB  Jfyoritj  etc  Areturtu  is  a  BooHb.  The 
reader  will  here  see  a  resemblance  to  our  way  of  designat- 
ing individuals  by  a  Christian  name  followed  by  the  fi^nily 
name.  The  Greek  letters  furnish  tiie  Christian  names  of 
the  aqpante  stars,  while  the  name  of  the  constellation  is 
that  of  the  family.  As  there  are  only  fifty  letters  in  the 
two  alphabets  used  by  Batkb,  it  will  be  seen  that  only  the 
fifty  bri|^test  stars  in  each  constellation  could  be  desig- 
nated by  tins  meihod.  In  most  of  the  constellations  the 
number  thus  ohoseiik  is  much  less  than  fifty. 

When  by  the  t&A  of  the  telescope  many  more  Btan  than 
these  wera<  laid  down,  some  other  mediod  of  denoting 
ihran  became  neeesMury.  Fi.Ai(8nncD,  who  obaerved  be- 
fore uA  after  1700,  prepared  an  extensive  catalogiu  of 
Stan,  in  which  those  of  eiioh  constellation  wererdesignated 
by  nnmben  in  the  order  of  right  ascension.  These  nam- 
ben  wow  entirely  independent  of  the  designations  of 
BAHn  fliat  is,  he  did  not  omit  the  Batbb  stan  from 
his  fyitem  of  nunben,  but  numbered  them  aa  if  they  had 
no  Gndc  letter.    Henoe  those  stan  to  w)uch  Batkr  ap- 


4S» 


ABTBONOMT. 


plied  letton  have  two  designatioiu,  the  letter  and  the 
number. 

Fi.AiifmtBD*B  nnmbera  do  not  go  much  above  100  for 
any  one  constellation — Taurut,  the  riehest,  haying  189. 
When  we  consider  the  q^ore  nomerons  minute  stara,  no 
systematic  method  of  naming  tliem  is  possible.  The  star 
can  be  designated  only  by  its  position  in  the  heavens,  or 
the  number  which  it  bears  in  some  well-known  catalogue. 


f,  4.    DMOBIFFIOir  OV  THE  OQNmOAATIONS. 

The  aspect  of  the  starry  heavens  is  so  pleasing  that 
nearly  every  intdligent  person  desires  to  possess  some 
knowledge  of  the  names  "and  forms  of  the  principal  ooa- 
steUations.  We  therefore  present  a  brief  description  of 
the  more  striking  ones,  illustrated  by  figures,  so  that  the 
reador  may  be  Me  to  recognise  them  when  he  sees  them 
<Hi  a  dear  nigbt. 

We  h^n  with  the  oonsteUations  near  the  pole,  beoanw 
they  ean  be  sem  <m'hny  dear  ni^t,  while  the  sonttiena 
ones  can,  for  tSie  most  part,  G6lj  be  seen  during  onrtain 
seasons,  or  at  oertun  hours  of  the  ni|^i  TheaoewnMnj- 
ing  %iire  shows  all  the  stars  within  60*  of  the  pole  fliP^i 
iff  tibe  fourth  magnitude  indnaive.  The  Bopun  wmf9nik 
aniBBd  the  maigin  show  the  meridiana  of  r^t  ■winiaion, 
one  for  tivwy  hour.  In  order  |q  lusn  1^ -mi^  jwpresinit 
the  northern  opnsteUatiens  ezad<l(f  99  ^ajr  axe^  H  inaat  be 
held  so  that  the  hour  of  sideraal  tbne  alwjiidh  lliftobaerrar 
is  looking  at  the  heavens  dudl  be  at  tliNiv|k)p  of  the  map. 
Sui^o^ng  the  observer  to  look  i^.nfaM  0-dook  in  the  even- 
ing, the  months  around  the  maigin  of  the  map  diow  the 
regions  near  the  senith.  He  has  therefore  onty  to  hold  the 
map  with  the  mtmth  upward  and  ftoe  the  nearth,  when  he 
will  have  the  n<Mihem  heavens  as  they  afpuint  taaeftk 
that  ib»  stars  near  the  bottmn  of  the  map  ^^  be  ent  oHf 
by  thehoriaon. 

The  first  oonsteUation  to  be  looirad  for  la  Vtm  Jfi|^, 


ww^wpiiwwiiaawKwwLj.uiJuk'wwi^^  ., 


etter  and  the 

bove  100  for 
;,  liaYing  139. 
inute  Stan,  no 
>le.  The  star 
le  heavens,  or 
>wn  catalogue. 

ItULTIOmi. 

pleasing  that 
poMCM  some 
prinoipal  ooa- 
desoription  of 
9S,  BO  that  the 
a  he  sees  them 


I  pole, 

the  aouthieni 
during  oMrtain 
lieaooomMiijr. 
the  pole  f||Mni 


k^i 


m^ftiVtiirt  be 
&tll»obMnper 
ip  of  the  map. 
lokintheeviNi- 
miip  diow  the 
ntytoholdtiw 
lai^,  when  he 


itffl  he  enl  etf 


I  VnaMifforf 


TBB  CONSTtCLLAl'lONa. 


433 


the  Great  Bear,  familiarly  known  as  "  the  Dipper  "  The 
two  extreme  stan.  in  this  constellation  point  toward  the 
poJe-3tar  as  already  exphuned  in  the  opening  chapter. 

Ur»a  Minor,  sometimes  caUed  « the  LitUe  Dipper,"  is 
the  oonsteUation  to  which  the  pole-star  belongs.    About 


itt—juf  «v  tarn 


wnaaajntutm. 


Ifi  ftom  the  pole,  in  fi|^t  aaeenskm  XV.  hoon,  is  a  star 

{*  ^•F'W  ■*»'    A  ottrved  row  of  three  small  stan  lies 
befcWt^B  ^#iM  t«o  bri^t  ones,  and  fonns  the  hwdle  of 


4M 


ABTRONOMT. 


Cassiopeia,  or  "  the  Lady  in  the  Chair,"  is  near  hour  I 
of  right  aBcension,  on  the  opposite  side  of  the  pole-star 
from  Ursa  Mtyor,  and  at  nearly  the  same  distance. 
The  six  brighter  stars  are  supposed  to  bear  a  rude  resem- 
blance to  a  chair.  In  mythology,  Cassiopeia  was  the  qneen 
of  CepheuSy  and  in  the  mythological  representation  of  the 
constellation  she  is  seated  in  tlie  chair  from  which  she  is 
issuing  her  edicts. 

In  hour  III  of  right  ascension  is  situated  the  constelU- 
tion  Perseus,  about  10°  further  from  the  pol«  than  Cas- 
siopeia.  The  Milky  Way  passes  through  these  two  con- 
stcjktbns. 

JDraoOf  the  Dragon,  is  formed  prindpalhr  of  a  bng 
mw  of  Stan  lying  between  Ursa  Mt^or  and  Ursa  Minor. 
The  head  of  the  monster  is  formed  of  the  nOTthemmoat 
three  of  four  bright  stars  arranged  at  the  ocwiiers  o£  a 
loeenge  between  XYII  and  XYIIIhous  of  xi^  aseen- 


Ctg^lmts  k  on  die  oppocite  side  U  Oasnegma  fnm 
Fmmm,  ^yb^  ia  tke  Mttky  Way,  about  XXH  honra  of 
i^^Wlwioii     Ukaiyl  a  brilliant  consteUation. 

^ttur  OMMtoHatfoBi  vm  the  pole  ant  Oamehg^f^tilu, 
i^mg,  and  Laeerta  \fS^  Liaard),  bat  they  oonlaiii  only 


01  daittiiilttgilM  MBdMm  eoMtelhifcioiia,  ira  itaU  Idee 
liMfW^im^lpB^^  atartj  ai^MW  cmjionding 

raapeo^^.  to  VX  kdwa,  ZU  hmms  XVIXl  hours, 
and  0  h«iin  el  iMacMl  time  or  figil  mmkm  Theae 
hours  of  ooniM  OQoiir.fiiiiy  da^,  tnift  not  always  aft  con- 
venient times,  teeanai  liiey  wj  with  the  tune  of  the 
year,  as  explained  in  Chapter  I.,  Part  I. 

We  shall  first  suppose  the  obeerrer  to  yie#  the  heavens 
at  YI  honrs  of  sidereal  time,  which  occurs  on.  Decem- 
ber aist  about  midnight,  January  1st  about  11.80  r.M., 
February  Ist  about  9.80  p.h.,  Haroh  Ist  about  7.80 
P.M.,  and  so  on  through  the  year,  two  hours  earBer  eveiy 
month.    In  this  position  of  the  sphere,  the  Millcy  Way 


pm4iii.iMi!Miiw!ife..ii,w!iiyiitL .  MM.  .u..K.iimm.\mm>i 


ig  near  hoar  I 
the  pole-star 
ime  liifltanoe. 
mde  reflem- 
was  the  qneen 
sntation  of  the 
u  which  she  is 

the  coiistelhi- 
wle  thaa  Cas- 
(hflie  twocon- 

aW  of  a  long 
1  UrM  Mmor. 
\  northummoBt 
)  oomars  o£  a 

f   Xi|^    UKKOk- 

XXUhoum  of 
aUation. 

y  oooy&<»l7 

mmfbiUtake 
mding 

XVIE  hoow, 
These 


THE  CONBTKLLATWNB. 


425 


ajtwaya  at  oon- 
le  time  of  tiie 

ci#  the  heavens 
lira  on.  Decein- 

Qt  11.80  P.M., 

Ut  about  7.30 
m  eurlier  every 
beMUkyWay 


spans  the  heavens  like  an  arch,  renting  on  the  horizon  be- 
tween north  and  north-west  on  one  side,  and  between 
south  and  south-east  on  the  other.  We  shall  first  describe 
the  constellations  which  lie  in  its  course,  beginning  at  the 
north.  C«pheu9  is  near  the  north-west  horizon,  and  above 
it  is  CoMtopeia,  distinctly  visible  at  an  altitude  nearly 
equal  to  that  of  the  pole.  Next  is  Peraetts,  just  north- 
west of  Hkb  stnitb.  Above  Pene/ut  lies  ^iirt^a,  the 
Chsriotetfi^  whidi  mqr  be  reeagniaed  by  a  brif^t  star  of 
the  first  mguitade  called  OoipSlla  (the  G<Mt),  now  quite 
>"  -  the  mnttli.  Amiga  b  represented  as  holding  a 
^^,  >  his  arms,  la  the  be  '.  '  which  the  star  is  situated. 
Abi>u.  10"  CMt  of  <Ay«^  IS  tlw  star  ^  A^tifim  of  the 
second  insgnitnde. 

Going  firihsr  south,  tiie  Mitty  Way  next  passes  between 
Tamrug  tilA  0«mM» 

Tawmt  th*  Bun,  magr  1»  rsoegnked  hf  Ihb  Pleiades, 
or  "  Sev«i»  6t««*"    Bwlfy  than  avs  only  sk  slws  in  the 

group  cimi^'dAis  m-mit' 

nary  eyes^  iN#ia|r  iy»4ln^ 
enough  tf  ^tiiil;  «II|(M|n 

ably  see  't^fmmf^mm 

in  all.  lib  mm0'"§atm  Ml 
interestiq|r  «|^e9l  «f  iHt&a^ 
with  a  miiBtwiiiiiniiii  mibtty 
oreigh<y#iii<ipi|fe 
be  seen.  ':':W^^^0lltlkillM^  finp' 
sent  a  trilii»iii^'#i^  slit|j^ 
the  six  hiiq[|i«lMi  itfa«  «hati 
visible  to  any  indinary  ey«| 
the  five  next  in  size  tbose 
whieh  caa  be  seen  by  a  re> 
nuurlably  good  eyoy  sad  the 
others  ttioee  wHoh  reqidre  a  telescope.  East  of  the  Pleia- 
des is  UmT  br^^  red  star  Aldebarany  or  "  the  Eye  of 
thia  BnB.*'  It'Hes  in  a  group  called  ihe  ffyadee,  ar- 
rtaigeA  ia  the  f<Mmi  of  the  letter  Y,  and  forming  the  face 


Via.  I'lli  ""'I'BbModVK  vnw  ov 
tarn  FMUPM. 


42U 


ASTBONOMr. 


of  the  Bull.  In  the  middle  of  one  of  the  legs  of  the  V 
will  be  seen  a  beautiful  {tair  of  stan  of  the  fourth  magni- 
tude very  close  together.     They  are  called  0  Tauri. 

Geminiy  tlie  Twins,  lie  eaat  of  tlie  Milky  Way,  and 
may  be  recogniied  by  the  bright  stara  Ctutor  and  PoUvaSf 
which  lie  90°  or  SO**  aonth-eaat  or  south  of  the  senith. 


They  are  about  5**  apart,  and  PoUum,  the  sonthemmfwl 
one,  ig  a  little  brighter  than  Oattor. 

Orum^  the  moet  brilliant  eorateHation  in  the  heavens, 
is  very  near  the  meridian,  lying  sonth-east  of  Tamtu  and 
souih-weet  of  Oemmi.  It  may  be  readily  ieo(^;niaed  by 
the  figure  iHiicli  we  give.     Four  of  its  bright  akan  fonn 


wmm 


wimmmmmmm^'mmmiim 


legs  of  the  V 
fonrth  magni- 
9  Tauri. 
Iky  Way,  and 
tr  and  PoUwDf 
of  the  zenith. 


D  ionihenmuiil 

n  the  heavens 

of  Tannnf  and 

reoogniaed  by 

akan  form 


TUK  VONaTKLLATlONO. 


m 


a  rectangle  about  15°  long  from   north 
°  wide.     In  tliu  middle  of  it  is  a  row  of 


tlio  comerH  of 

to  south,  and  h''  wmo.  in  uiu  miuaie  oi  ii  la  a 
three  bright  stara  of  the  second  magnitude,  whicJi  no  one 
can  fail  to  recognize.  Below  this  is  another  row  of  three 
smaller  ones.  The  middle  star  of  this  last  row  is  called 
t)  OrioniSf  and  is  situated  in  the  midst  of  the  great  nebula 
of  Orion,  one  of  the  most  remarkable  telescopic  objects  in 
the  heavens.  Indeed,  to  the  naked  eye  tliis  star  has  a 
nebulous  hazy  appearance.  The  two  stars  of  tlie  first 
magnitude  are  a  Orionu,  or  Betdgftete,  which  is  the  high- 
est, and  may  be  recognized  by  its  red  color,  and  Jiiyd, 
or  fi  Ortonit,  a  sparkling  white  star  lower  down  and  a 
little  to  the  west.  The  former  is  in  the  shoulder  of  the 
figure,  the  latter  in  the  foot.  A  little  north-west  of 
JtetelgtMm  9X4  Haee  (mMll  itan,  whioii  form  llie  head. 
The  row  of  atam  on  the  WMt  lonu  his  una  toad  elub,  the 
latter  beiagniiedl  •§  if  t»  iM&e  at. Tamm,  ifae  Bull,  on 
the  west. 

Cants  m^r,  tlw  UMb'  BOf,  Mm  «araM  the  Milky 
Way  {mm  Onm^  $aA  tm^  be  HBQjpliiiil  bgr  ^  bright 
star  Prttmm  ni-  lk»  im/k  lUgilriMK.  Tk»  Hfee  stars 
PoUwe,  frmffm,miJBkifii$\tmmim  •  rigbt  Wgled  tri- 
angle, th»  fldit  aa|^  bifa«  it  Phv^m. 

CanUm^^mOmlJi^lkf^flVfm'mlk^  Orion, 
and  is  easily  raeoipiiaed  bj  8irw9,  Uie  brightest  fixed  star 
in  the  heevens.  A  number  ef  bl^t  stars  south  and 
south-east  ef  JSirim  bdoag  to  this  oonsteUati(Hi,  making 
it  one  of  gnat  htSXmuBj. 

Argo  Namt  the  ship  Argo,  Ifisneer  the  south  horizon, 
partly  above  it  and  partly  bebw  it.  Its  brightest  star  is 
Camopm,  which,  next  to  l^riva,  is  the  bri^test  star  in 
the  heavens.  Being  in  68**  of  south  dedinttdon-,  it  never 
rises  to  an  observer  within  58**  of  the  North  Pole— that  is, 
north  of  87**  of  north  latitude.  In  our  country  it  is  visi- 
ble only  in  the  Southern  States,  and  even  there  only 
between  six  and  seven  hours  of  sidereal  time. 

We  next  trsoe  out  the  zodiacal  ecmstelktions,  which  are 


«lB>K»^Jf  LUIJW  'WW  i  I 


4^8 


ASTBONOMY. 


Of  interoBt  hocaiwo  it  is  through  thorn  that  the  gnn  ««««, 
in  Its  apparent  annual  cou«e.  We  shall  commence  in 
the  west  and  go  toward  the  east,  in  the  order  of  riirht 
ascension.  ® 

Ariety  the  Ram,  is  in  the  west,  about  one  tliird  of  the 
way  from  the  horizon  to  the  zenith.  It  may  be  leoognized 
by  three  stars  of  the  second,  tliird,  and  fonrthmairni- 
tudes  rosiwtively,  forming  an  obtuse-angled  triable. 
The  brightest  star  is  the  highest.  Next  toward  thTLt 
IS  Tm*rm,  the  BuU,  which  brings  us  nearly  to  the  meri- 
dian, and  east  of  tlie  meridian  lies  Gemini,  the  Twins,  both 
of  which  oonstelktions  have  just  been  described 


-ra«  wanaujMom  uo,  thb  lk». 


K-    P      ^^'^ '"^^"o'^^orthy  object  in  this  constel- 

Leo,  tiie  Lion,  Ig  from  one  to  two  hoan  above  the 
««temhonzon.  Ite  brightest  star  is  i?i,^,1^rtWrf 
of  the  way  from  the  eastern  horizon  to Xlenith,  wd 

BtaiB  north  of  It  m  a  curved  line  are  in  the^  form  of  a 


THK  VONSTKLnATJONft. 


4iQ 


3in  tliat  the  snn  pames 
Vo  sliall  ooininenoe  in 
,  in   the  order  of  right 

abont  one  tliird  of  the 
.  It  may  be  reoognized 
rd,  and  fourth  inagni- 
>btu0e-angled  triangle. 
Next  toward  the  east 
OS  nearly  to  the  ineri- 
emini,  the  Twins,  both 
len  deaeribed. 


Lao,  TBI  uov. 

nini,  but  oontainR  no 
object  in  this  conatel- 
}pio  Stan,  which  ap- 
inilky  light.  To  we 
the  moon  not  in  the 

wo  hours  above  the 
is  Btgul/M^  one  third 
to  the  zenith,  and 
titudes.  Five  or  six 
in  the^  form  of  a 


Hu^klo,  of  which  lieg^du*  ia  the  handle.  As  the  Liun  w»m 
(Iniwn  among  thu  old  uonHtolliitionH,  HeanluH  forinud  hiH 
liuart,  and  wae  thoroforu  callud  (hr  Leon'm.  Thu  Mukle 
fonna  Im  head,  and  his  body  and  tail  extend  toward  the 
horizon.  The  tail  ends  nonr  the  atur  Detiebda,  which  is 
quite  near  the  horizon. 

Leo  Minor  lies  in  the  north  of  Leo,  and  Sewtaiu,  the 
Sextant,  sontli  of  it,  but  neither  contains  any  bright  stars. 

J^ridantts,  the  Itivcr  Po,  south-west  of  Orion  ;  Lqms^ 
the  Hare,  south  of  Orion  and  west  of  OantM  M<yor ; 
Oflumba,  the  Dove,  south  of  Leptts,  are  constellations  in 
the  south  and  south-west,  which,  however,  have  no  strik- 
ing features. 

The  conacelUtions  we  }iave  described  are  those  seen  at 
fiix  hours  of  sidereal  time.  If  the  sky  is  observed  at  some 
other  hour  near  this,  we  may  find  the  sidereal  time  by  the 
rule  given  in  Chapter  I.,  g  S,  p.  80,  Mid  allow  for  the  di- 
urnal motion  during  thd  interval. 

AppoMMiiM  Of  Mm  OooateUaMima,  st  IS  Houk)  Sidereal 
Time.— This  hour  oocura  on  April  1st  at  11.80  p.m.,  on 
May  1st  at  9.80  r.M.,  aud  on  Juno  lat  at  7.80  p.m. 

At  this  hour,  dm  Mqfor  is  near  the  senith,  and  Oaui- 
irpeia  near  or  bebw  the  north  hinteoB.  mutWfkj  Way 
is  too  near  the  horiz<m  to  be  visMs.  gaabu  lis  ia*  in 
the  west,  and  there  is  no  very  oonapionons  oonifeHattoii 
in  the  south.  CaOor  and  Polhm  are  high  np  fai  Hie 
north-west,  and  Prooyon  is  abcmt  aa  howr  and  a.  liilf 
above  the  horizon,  a  little  to  the  aowft  of  went  AO  Ae 
oonsteUations  in  the  west  and  nortb-w«at  have  Imb  pnnri- 
ously  described,  Leo  being  a  little  west  of  the  merUfan. 
Three  zodiacal  constellations  have,  however,  risen,  wliich 
we  shall  describe. 

Virgo,  the  Virgin,  has  a  single  bright  star,  Spica, 
about  as  bright  as  Regvihu,  now  about  one  hour  east  of 
the  mwidian,  and  but  little  more  than  half  way  from  the 
zenith  to  the  horizon. 

labrOf  the  Balance,  is  south-east  from  Virgo,  but  lias 
no  oonsjncuons  stars. 


480 


AHTRONOMY. 


SoftrpitM,  tlio  Scorpion,  m  just  rirting  in  tho  Houtti-eMt, 
Init  iH  not  yet  high  un«»ngh  to  Ih)  well  ttuun. 

Jlydrti  \»  II  vury  long  conHtelUtion  oxtunilitig  from 
Cvuiit  Minor  in  a  8outh-ua«t  diroction  to  the  Bonth  liori- 
son.  Itg  brightost  star  is  a  Jlydra,  of  tliu  aeoond  magni- 
tude, 85°  bolow  lieffulua. 

Corvus,  tho  Grow,  in  Ronth  of  Virffo,  and  may  l>o  ruc^ig- 
nisod  by  four  or  five  stans  of  tho  Bocond  or  third  magni- 
tude, 15°  Bouth-west  from  «^p«a. 

Next,  looking  north  of  the  zodiacal  oonfltollations,  we 
see : 

Coma  Berenices,  the  Hair  of  Berenice,  now  exactly  on 
tho  meridian,  and  about  10°  south  of  tho  zenith.  It  is  a 
dose  irregular  cluster  of  very  small  stars,  unlike  any  thing 
elflo  in  the  heavens.  In  ancient  mythology,  Berenice  had 
vowod  hor  hair  to  Venus,  but  Jupiter  carried  it  away  from 
the  temple  in  which  it  was  deposited,  and  made  it  into  a 
constellation. 

Bootes,  the  Bear-Keeper,  is  a  laage  constellation  east  of 
Coma  BeremoM.  It  is  marked  by  Arcturuty  a  bright  but 
somewhat  red  star  of  the  first  magnitude,  about  20°  east 

of  the  zenith.  Bootes  is  repre- 
sented as  holding  two  dogs  in  a 
leiiflh.  These  dogs  are  called 
Canes  VenaUei,  and  are  at  the 
time  supposed  exactly  in  onr  ze- 
nith chasing  Ursa  Mt^or  around 
the  pole. 

Corona  Borealis,  the  North-. 

em   Crown,   lies  next'  east   of 

Bootes  in  the  north-east      It  is 

"^'  a  bmall  but  extremely  beantiftil 

constellation.     Its  principal  stars  are  arranged  in  the  form 

of  a  semicircular  chaplot  or  crown. 

Appaannoe  of  the  OonateUationa  at  18  Howni  of  8ida- 
roal  Time. — This  hour  occurs  on  July  1st  at  11.80  p.m., 
on  August   Ist  at  0.30  p.m.,  and  on  September  Ist  at  7.80 

P.M. 


FH.  IM.— ooKniA. 


77/ A'  rONSTKLLATlONff. 


481 


tllO  HOUth-OMt, 

xtuiuling  from 
bhe  Bunth  hori- 
J  aeound  inagnt- 

d  may  »>o  rowig- 
ir  third  magni- 

oiwtellations,  we 

,  now  exactly  on 
I  zenith.  It  is  a 
unliko  any  thing 
;y,  Berenice  had 
ried  it  away  from 
d  made  it  into  a 

natellation  east  of 
mu,  a  bright  bat 
I,  about  30°  eaat 

Boottt  ia  repre- 
ig  two  doga  in  a 

dogs  are  called 
I,  and  are  at  the 
Bxactly  in  oar  ae- 
I'M  Mt^or  aroand 

00^,  the  North- 
68  next'  east  of 
north-east  It  is 
tremely  beantifal 
mged  in  the  form 

.8  Hows  of  Bi'ds- 
Bt  at  11.80  p.ii., 
temberlstatT.SO 


Tn  tills  position,  tlio  Milky  Way  hchmiih  oih-o  moru  to 
H|MUi  tlio  lii'HVuiiH  liico  nil  nn^h,  reHtiii^  mi  tlio  liori/.oii  in 
tliu  north-woHt  and  Huiitli-voHt.  lint  wu  do  not  suo  tlio 
same  parts  of  it  which  were  viHihIe  in  the  first  position  at 
rIx  hours  of  right  aenonsion.  (Aumopeia  is  now  in  the 
north-east  and  (/rta  Majw  has  passed  orer  to  the 
west. 

Arcturut  is  two  or  throe  honrs  above  the  western  hori* 
7!on.  We  shall  commence,  as  in  the  flist  position  of  tlie 
H[)here,  by  describing  tho  constellations  which  lie  along  on 
tlio  Milky  Way,  starting  from  Casaiopeia.  Above  Cam' 
npeia  we  have  GepAeut,  and  then  Zaotrta,  neither  of 
which  contains  any  striking  stars. 

Ojfgnwtf  the  Bwan,  may  be  recognised  by  limr  or  five 
Htara  forming  a  cross  direotl;  in  the  centre  of  Jie  Milky 
Way,  and  a  sliort  distance  north-east  frrtni  the  zenith. 
The  brightest  of  these  stars,  a  OygrU,  forms  the  northern 
end  of  the  cross,  and  is  nearly  of  tiie  first  inagnitnde. 

Lyra,  the  Harp,  is  a  beantifal  const  -/.Ation  sr.  th-wwit 
of  Oygimt,  and  nearly  in  the  zenidi.  It  oor  'ns  the 
brilliant  star  Vega,  or  « 
Jjjfntf  9m.  nw  9nl  mi| 
nIttkK  and  of  i  \kMt 
wMto  eokr.  Soalli  oC> 
Fsfi  «•'  fmu  Mm  d\ 
th*  JmoA  HMgnM 
fMnlly  Ml  flUiqaB  pii»i  ^ 
aUalogHm,1ignAfek1te^ 


iMk  117.— I.TBA,  nofkiAi 


%■, 


iMil 


star  ol  the  pAniltelognuny  is  «  Lyrm,  a  very  interesting 
object,  beoaase  it  is  really  oompoeed  of  two  stars  of  the 
fonrth  nugnitade,  whica  ■%::  be  seen  separately  by  a  very 
keen  eye.  The  power  u«  ;>  u  this  star  doable  is  one  of  the 
best  tests  of  the  acnteness  of  one's  vision  (see  Fig.  122). 


s^ 


fW.tltH<,W}l»^W 


wU 


I- 


4.32 


A8TRONOMT. 


ftB.  116.— A^riLA,  inn.pin 

K us,  AMD  flASITTA. 


AquUa,  the  Eagle,  is  the  next  striking  constellation  in 
the  Milky  Way.     It  is  two  hours  east  of  the  meridian, 

and  about  midway  between  the 
zenith  and  horizon.  It  is  readily 
recognized  by  the  bright  star 
AUair  or  a  AguUa,  situated  be- 
tween two  smaller  ones,  the  one 
of  the  third  and  the  other  of  the 
fourth  magnitude.  The  row  of 
three  stars  lies  in  the  centre  of 
the  Milky  Way. 

SagiUa,  the  Arrow,  is  a  very 
small  constellation,  formed  of 
three  stars  inamediately  north  of 
AquUa. 
Ddphimuj  the  Dolphin,  is  a 
striking  little  constellation  north-east  of  AquUa^  neog- 
nized  by  four  stars  in  the  form  of  a  lozenge.  It  is  famil- 
iarly called  "  Job's  Coffin." 

In  this  position  of  the  oelestial  sphere  three  new  sodia> 
n\  constellations  have  arisen. 
;#)i«yMM,    the   6eofpkmt 

M  iboti  80**   abovw  Hki 
i0»m,  b  ^(oito  a  hmM 

itfim,  ot  m  Soor^t  %  ied> 
^:iiar  fl<  aevlj  tlw  ftml 
WMJlitftiiH  and  «  imig  VMrj 
of  eitrved  stars  west  of  it. 

Sagittarius,  the  Archer, 
comprises  a  large  collection 
of  second  magnitude  stars  in 
and  near  the  Milky  Way, 
and  now  very  near  the  meridian, 
form  the  arrow  of  the  archer. 


119.-HK)oiiniii,  tm  KOR- 
?io». 

The  weiternmoflt  stars 


king  constellation  in 
8t  of  the  meridian, 
lidway  between  the 
>rizon.  It  is  readily 
by  the  bright  star 
AquUcB,  situated  be- 
naller  ones,  the  one 
md  the  other  of  the 
itnde.  The  row  of 
ies  in  the  centre  of 
ay. 

le  Arrow,  is  a  very 
illation,  formed  of 
imiediately  north  of 

,  the  Dolphin,  is  a 
1  of  AgiMa,  recog- 
Msenge.    It  is  famiU 

)re  three  new  aodia- 


-HMxmpnm.  tmm  secNt- 
?ioir. 

w  weiternmoBt  stara 


THB  00N8TBLIATI0N8. 


488 


Caprioomm,  the  Goat,  >8  now  in  the  south-east,  but 
contains  no  bright  stars.  Aquarivs,  the  Water-bearer, 
which  has  just  rken,  and  Pmom,  the  Fishes,  which  have 
partly  risen,  contain  no  striking  objects. 

Ophiuchm,  the  Serpent-beurer,  is  a  very  huge  constel- 
lation north  of  Scorpitu  and  west  of  the  Milky  Way. 
Ophiuchvs  holds  in  his  hands  nn  immense  serpent,  lying 
with  its  tail  in  an  opening  of  the  Milky  Way,  south-west 
of  Agnila,  while  its  head  and  body  are  formed  of  a  ^1- 
lection  of  stara  of  the  third  and  fourth  magnitudes,  at- 
tending north  of  Soorphu  nearly  to  Sootet. 

IfereuletiBtLyery 
large  constellation 
between  Co rona 
Jiorealis  and  Z^r<(. 
It  is  now  in  the 
zenith,  but  contains 
no  bright  staiB.  It 
has,  however,  a 
number  of  interest- 
ing telescopic  o^ 
^»6ta,  among  tha^ 
the  great  ehiter  of, 

^*>  *a£^  ^'^'*— w 

tntlmoitooai^cfiiiiaMofBtan.     The  head  of  2?^vw», 
afaviu^  dtittlbed,  il  jolt  iioitii  o 

OmlMlitlttlli  rum*  •»  O  Hmm  of  BMmpmI  nua.  — 
This  tine  wffl  octenr  oti  October  1st  at  11.80  p.m.,  on 
Ifxiifimhur  1st  «t  9.80  r.it,  on  December  1st  at  7.80  km., 
aid  oil  Stftixmtym  at  6.80  p.m. 

In  this  position,  fheMilky  Way  appears  resting  in  the 
east  and  west  horisons,  but  in  the  cenith  it  is  incHned 
over  tpwud  the  north.  All  the  opnsteUations,  either  in 
or  north  of  its  ootnae,  are  among  those  already  described. 
We  shaU  therefora  oondder  only  those  in  the  south. 


I!.*  umi'imiu 


434 


A8TR0NOMY. 


Pegtuut,  the  Flying  Hone,  is  distingnished  by  four 
Btan  of  the  second  magnitude,  which  form  a  large  square 
about  16°  on  each  aide,  called  the  square  of  Pegemu.  The 
eastern  side  of  this  square  is  almost  exactly  on  the  meri- 
dian. 

Andromeda  is  distinguished  by  a  row  of  three  or  four 
bright  stare,  extending  from  the  north-east  corner  of 
Pegcufusy  in  the  direction  of  Peraem. 

CeiuSf  the  Whale,  is  a  large  constellation  in  the  south 
and  south-east.  Its  brightest  star  is  fi  Cetiy  standing 
alone,  80**  above  the  horizon,  and  a  little  east  of  the 
meridian. 

Pmcm  Auttrality  the  Southern  Fish,  lies  further  west 
than  CMwr.  It  has  the  brin^t  star  FomalhanUy  about 
16"  aboTe  the  horison,  and  an  hour  west  of  the  meridian. 

IB.    VUMBntnrOAVDOATAZiOOIIIirOTHB  STABS. 

As  teleaoqnc  power  is  increased,  we  still  find  stars  of 
lunter  and  fainter  Ught.  But  the  number  cannot  go  on 
ineNMring  forever  in  tfie  same  ratio  as  with  the  brighter 
nuf^i^iidaa,  beeaoae,  if  it  did,  tiie  whole  sky  would  be  a 
blaM  of  itariiglit. 

If  lel«no|MS  with  poipm  far  eoEfleeding  ow  preaent  ones 
wera  made,  they  would  no  doubt  show  new  stan  of  the 
90ih  and  Sltt  magnitndea.  But  it  is  highly  pfobaUe  thai 
the  iMMNJtfr  of  mxii  aaooeinve  order*  of  atan  wonld  not 
increaie  in  the  same  ratio  as  is  observed  m  the  8th,  Mi, 
and  10th  magnitudes,  fw  example.  The  eneaBoaa  labor 
of  eatimatmg  the  number  of  itan  of  ao^  elMMas  will  loi^ 
prevent  the  aoenmnlalMMi  of  atatbtioi  <m  tibia  qneitiim ; 
but  thiamueh  is  oertain,  that  in  i^eoial  r^gioM  of  tko  ihy; 
which  have  been  seawhingly  examined  by  vaifaMa  tele- 
aoopea  of  anoeeaaively  inemaaing  lyartiina,  the  nnn^ar  of 
new  stars  found  is  by  no  meao*  in  propMiioii  to  Hbm 
ineraaaed  inatmmental  power.  Tkm,  in  ^  eaitnl  por- 
tions of  the  nebula  of  Qritny  oaSkj  aome  half  dcnm  sla« 


MB!sei!KH»4#!>.yA-  :ism" 


nished  by  four 
a  large  square 
PegatfM.  The 
r  on  the  meri- 

three  or  four 
sast  corner   of 

n  in  the  sonth 

CeUf  Btanding 

■\e  east  of  the 

as  fortiherwest 
nalhmU,  about 
t  the  meridian. 

}THS8TAB8. 

lill  find  stars  of 
it  cannot  go  on 
ith  the  brighter 
sky  wOTild  be  a 

Mur  present  ones 
«w  Stan  of  the 
ly  prdbdde  tiiaft 
■tanwoidd  not 
in  the  8th,  9tfa, 
•noRMNU  labor 
elMMawmkng 
k  tins  qiMitioa; 

{iaiMoltt»iky« 
by  TaikiM  tfle* 

lytheiiiiB^at 
opMrtJon  to  ikm 
tiw  oastml  por- 
halldoMi 


CATALOQUmO  THE  STABS. 


486 


have  been  found  with  the  Washington  26-inch  refractor 
which  were  not  seen  with  the  Cambridge  15-inch, 
although  the  visible  magnitude  has  been  extended  from 
16"  •  1  to  IB"  -3.  If  this  is  found  to  be  true  elsewhere,  the 
conclusion  may  be  that,  after  all,  the  stellar  system  can  be 
experimentally  shown  to  be  of  finite  extent,  and  to  contain 
only  a  finite  number  of  stars. 

We  hare  alraady  stated  that  in  the  whole  sky  an  eye  of  aTerage 
power  will  aee  about  6000  stars.  With  a  telescope  this  numberia 
greatly  increased,  and  the  most  powerful  telescopes  of  modem  times 
will  {wobably  show  more  than  80,000,000  staiB.  As  no  trustworthy 
estimate  has  ever  been  made,  there  is  great  uncertainty  upon  this 
point,  and  tiie  actual  number  may  range  anywhere  Mtween 
1S,000,000  and  40,000,000.  Of  this  numbeB,  not  one  out  of  twenty 
has  ever  been  eatuogoed  at  alL 

The  gradual  increase  in  the  number  of  stars  laid  down  in  Tarious 
of  the  older  citaloguea  is  exhiUted  in  the  following  table  fhun 
CHAianas's  Bmer^^tiM  AMronomf : 


OoMmUtA- 
noK. 

Ptotaur. 
b.o.m6l 

Tyeho 

Bnhe. 

A.D.lBni. 

.  HeTCliaa. 
AJkUSO. 

FiMMtaed. 
A.O.  law. 

Bode. 
A.D.  1800. 

Aries 

Una  lii^r.. 
Bofltes...  . . 

Leo 

Vlrga...... 

Tanms 

Orion. 

18 
85 
88 
85 
88 
44 
88 

81 
56 
88 
40 
88 
48 
68 

87 

78 
58 
60 
80 
51 
88 

66 

87 

81 

>       80 

110 
141 

78 

148 
888 

818 

8»« 

804 

The  most  fanooa  and  extrndve  aeriea  of  star  obsenrations  are 
noticed  bdov. 

The  aaaBOBMtrks  of  Batkb,  FLAnraDi,  AaaBi.An>n,  Hlns,  and 
Qoou»|^etlM  lodd  stars  of  oaeorbotii  hoiynhafw IsMdowa 
OBmi^  1Wanjqvl»ntedbf  th«  star  ot^alagoM  of  other 
observwi,^wildiacniitnBnbwhMbeeapBUished.  TliMalait 
were  undstlalani  Budafy  for  tiM  dateradnattcm  of  alar  piMilioBa  btit 
tiMjr unrifar^va  is  an  aoalllaigr datna  Hu mageitaat of  tke star 
obaawsd.  Whm  tiiqr  v  mnkA  so  fv  as  to  corer  the  hMvaaa, 
they  will  aflofd  nlaaUa  data  as  to  the  dislribatkm  of  ttUm 


The 


- . .„  of  stars  nt  coMUiltisd  ia  ttM 

in  mrMekm  OmHmtm  ammilt,  tha  jsls*  irwfc 

mA  hh  ■■islMls,  mammm  mt  Baritafmo.    It 

tfcasfaai  tha  lut  ai—  mMMitadsa  iftw  th»  North 


iei*w>e«M>;if«(ri: 


sum 


mm 


sm 


486 


ABTBONOMT. 


Pole  to  8*  of  MNith  decliDstion.  This  work  wm  tiegun  in  18S9,  and 
At  its  completion  a  cstalogue  of  tlie  approximate  places  of  no  lesB 
than  814,926  stars,  with  a  series  of  sUr-maps,  giving  the  aspect  of 
the  northern  heavens  for  1855,  was  published  for  the  use  of  astrono- 
mers. Aboblamdbh's  ori^nal  plan  was  to  carry  this  DurekmuOerunif 
as  far  as  28"  south,  so  that  every  star  visible  in  a  small  comet-seeker 
of  Sf  inches  aperture  should  be  registered.  His  ori^nal  plan  was 
abandoned,  but  his  former  assistant  and  present  successor  at  the 
observatory  of  Bonn,  Dr.  BoBdMraLD,  is  now  engaged  in  executing 
this  important  work.  ....        .    ,      .     ..     .  , 

The  Catalogue  of  Stars  of  the  British  Association  for  the  Ad- 
vancement of  Science  contains  8877  stars  in  both  hemispheres,  and 
gives  all  the  stars  visible  to  the  eve.  It  is  well  adapted  to 
team  the  unequal  distribution  of  the  ludd  stars  over  the  celestial 
sphere.    The  Uble  on  the  opposite  page  is  formed  from  its  data. 

From  this  table  it  follows  that  the  southern  sky  has  many  more 
Stan  of  the  flnt  seven  magnitudes  than  the  northern,  and  that  the 
lones  immediately  north  and  south  of  the  Equator,  although  greater 
in  surface  than  any  others  of  the  same  width  in  declination,  are 
absolutely  poorer  in  such  stars. 

Tlie  meaning  of  the  table  will  be  much  better  understood  by  con- 
suiting  the  graphical  representation  of  it  on  page  488,  by  PiiooTon. 
On  tSs  chart  are  laid  down  all  the  stars  of  the  British  Association 
Catalogue  (a  dot  for  each  star),  and  beside  these  the  Milky  Way  is 
represented.  The  relative  richness  of  the  various  sones  can  be  at 
once  seen,  and  perhaps  the  scale  of  the  map  will  allow  the  student 
to  trace  also  the  zone  of  brighter  stars  (lst-8d  magnitude),  which  is 
inclined  to  that  of  the  Milky  Way  by  a  few  degrees,  and  is  approx- 
imately a  great  circle  of  the  sphere.  ^ 

The  distoibntion  and  number  of  the  brishter  ntars  (1st- 7th  mag- 
nitude) can  be  well  understood  from  this  cbart. 

In  Aboblaiidbb'b  Durekm«$t«rHnf  of  the  stars  of  the  northern 
heavens,  there  are  recorded  as  belonging  to  the  northern  hemi- 
sphere : 

10  stem  between  the  1  0  magnitude  and  the  1  -9  Dugnltode. 


87 

U 

t« 

9^0 

•1 

If 

198 

u 

«« 

80 

M 

M 

810 

tt 

u 

40 

M 

«< 

i.oie 

«« 

u 

50 

M 

<« 

-888 

•( 

tt 

00 

■I 

W 

18.808 

*4 

«■ 

70 

<• 

M 

67,900 

u 

4( 

80 

tt 

•4 

89 

987.544 

l« 

•« 

90 

U 

If 

9-6 

In  all  814,996  stars  from  the  ilrst  to  the  9-6  oMgnitodea  ara  «m»- 
merated  in  the  aorthmn  sky,  so  that  tlMN  are  aboot  600^000  in  tfie 
whole  heavena. 

We  nay  nadUy  compute  the  aaoank  of  Ii|^t  raerived  by  tba 
evthoB*  dear  but  aMMiileasnli^tftomaMaeetei.  U^vmwmamt 


mmsimtrnfii^mi^immsii^imi' 


I  begun  in  18S8,  and 
ate  places  of  no  lesa 
^▼ing  the  iwpect  of 
tr  the  nae  of  astrono- 
this  DurehmuUemng 
i  small  comet-seeker 
[g  original  plan  was 
int  successor  at  the 
Dgaged  in  executing 

KMsiation  for  the  Ad- 
ith  hemispheres,  and 
is  well  adapted  to 
trs  over  the  celestial 
oed  from  its  data. 
I  sky  has  many  more 
rthem,  and  that  the 
or,  although  greater 
li  in  declination,  are 

r  understood  by  con- 
ge 488,  by  Pbootor. 
B  British  Association 
)se  the  Milky  Way  is 
nous  zones  can  be  at 
rill  allow  the  student 
magnitude),  which  is 
greea,  and  is  approx- 

r  i«t«rs  (Ist-Ttti  mag- 

ian  of  the  northern 
)  the  northern  hemi- 


thel-OmagnUode. 

8» 

ts 

9-9 

<■ 

48 

It 

5«« 

«l 

99 

«• 

7-9 

m 

8-9 

H 

9-5 

•« 

I  awgaitodM  am  wn» 
BtlMiat  600^000  in  the 

Ol^t  rsedved  hf  tlia 
>etan.  LetustMinM 


»    1^ 

a 


oe 


§ 


s 


<» 


DiaTRIBUTlOJr  OF  STARS. 


Il9  M  ^^  N^  ^  H*  h^  HA  ^A  M  t^  ^  ^ 

iliittittttnitiitnil 


437 


at  «o  oe  1^  ee «»  ee  4)  i-i  iK  A  iK  ee  M  iK  CN  fl»  M  ei  00 -4  A  S^  !^ 


K  to  *t  ^  ***'-*>*' *^  I-*  *!*<•*        h' Ca  I-*  >-' 1^  I-*  I-*  k^  tS  k' 


+   + 

?^5 


+  + 


£ssit'ji$sis{s^sesss;:s!Ss^ss!Sisss^s 


SSiSSS3SSS£3£S8S;:iSS!SSSSI!S£38g^S§ 


+  + 


SS«;$igg{SIS£SSS33£l^;§^3SS3:3SS;j£S 


^SSg£SS::;!SS££S!gSSS:82i$SSi£;SI§^JSi 


+  + 


!i:S8S6£S!SSS!£:S£$^^S^SS6£Srg 


«5ssssssss^s;r,tiS£s:sitsS£tg!^{3SS= 


.'»+ 
«<"? 


i'i 


:33S£S£;SStSlgSS3SS!^tt@S 


S66S8SSSSt8SSS888SSS;SSSSISSSS 


^'4 


• 1 — 


4DOOkaki^eiMeea-e«9o  ei-<«>*Miik-9ei>4«4>)e 


I     I 


I     I 


m%%%wm%u%in%%^um 


+  + 


% 
% 

n 

I 

5 

? 

e 


H 
R 
M 

W 

i 


^ 


MNMWMRM 


iw»ii«iMmi*wruKw>»fww^*-  "^ 


BRIOHTlfBBa  OF  THE  aTABS. 


430 


that  the  brightneia  of  «a  mrtHgo  itar  of  the  first  magnitude  ia 
about  0*5  of  that  of  a  Lj/ra.  A  itar  of  the  2d  magnitude  will  shine 
with  a  light  expressed  by  0-S  x  0'4=0-80,  and  so  on. 


Thetfital 

brightneia 

Of       10  1st 

magnitade  state  is    60 

•« 

H 

87  8d 

11 

7-4 

M 

M 

138  8d 

II 

101 

•< 

«* 

810  4th 

«i 

»-9 

N 

(1 

l.Olt  Sth 

' 

180 

M 

M 

4.8M«th 

t* 

881 

« 

M 

18,5M  7th 

IS 

87-8 

« 

•  1 

57.900  8tb 

•1 

47-4 

Sam  =  148-7 

It  thus  appears  that  from  the  stars  to  the  8th  magnitude,  inclu- 
sive,  we  recMTe  148  tioMs  as  much  light  as  from  a  Lyrm.  a  Lyra 
has  been  determined  bj  ZSixnu  to  be  about  44,000,000,000  times 
fainter  than  the  sun,  so  that  the  proportion  of  starlight  to  sunlight 
can  be  computed.  It  alio  appears  that  the  stars  of  nuupitudes  too 
high  to  aUow  them  to  be  indiTidually  Tisible  to  the  nidted  eye  are 
yet  so  numerous  as  to  affect  the  genenl  brightness  of  the  sky  more 
than  the  so-called  lucid  staia  (lsl-4tb  magmtude). 


■ii'mliiiMitttui.iMi 


|M««M)'M>S»i-."5W  if 


'm^/'.lm.-.a-  .-,■  •'Hi,  IT.HilM  )■  ^>i|iWWHll|i 


in 


CHAPTER   II. 

VARIABLE  AND  TEMPORABY  STABS. 

g  1.  8TAB8  BSQITLABLT  VABIABLB. 

All  Stan  do  not  shino  with  a  constant  light.  JSince 
the  middle  of  the  seventeenth  oentnry,  stars  variable  in 
brilliancy  have  been  known,  and  there  are  also  stars  which 
periodically  change  in  color.  The  period  of  a  variable  star 
means  the  interval  of  time  in  which  it  goes  through  all  its 
changes,  and  returns  to  the  same  brilliancy. 

The  most  noted  variable  stars  are  Mira  Ceti  (o  Cett) 
and  Algd  {ft  Persei).  Mira  appears  about  twelve  times 
in  eleven  years,  and  remains  at  its  greatest  brightness 
(sometimes  as  high  as  the  2d  magnitude,  sometimes  not 
above  the  4th)  for  some  time,  then  gradually  decreases  for 
about  74  days,  until  it  becomes  invisible  to  the  naked  eye, 
and  so  remains  for  about  five  or  six  months.  From  the 
time  of  its  reappearance  as  a  lucid  star  till  the  time  of  its 
maximum  is  about  43  days  (Hkis).  The  mmm.  period,  or 
the  interval  from  minimum  to  minimum,  is  about  333 
days  (Aboblandkr),  but  this  period,  as  does  the  maxi- 
mum light,  varies  greatly. 

Algd  has  been  known  as  a  variable  star  since  1667.  Its 
period  is  about  ^  20^  49",  and  is  supposed  to  be  from 
time  to  time  subject  to  slight  fluctuations.  This  star  is 
commonly  of  the  2d  magnitude ;  after  remaining  so 
about  2i  ^uw,  it  falls  to  4"  in  the  short  time  of  4^  hoursi 
and  T9m0»  of  4°>  for  80  minutes.  It  then  commences 
to  increase  in  brilliancy,  and  in  another  3|  hours  it  is 


STARS. 

ABUB. 

light.    Since 

ire  variable  in 

Iso  stare  which 

a  variable  star 

through  all  its 

(  Ceti  (o  Cell) 
*,  twelve  times 
est  brightness 
sometimes  not 
y  decreases  for 
the  naked  eye, 
18.  From  the 
^e  time  of  its 
vean  period,  or 
,  is  about  338 
loes  the  i&axi- 

inee  1667.  Its 
k1  to  be  from 
This  star  is 
remaining  so 
le  of  4^  houiBi 
en  commences 
^  houn  it  is 


VAItTABLS  8TAR8. 


Ul 


again  of  the  2d  magnitude,  at  which  point  it  remains  for 
the  remainder  of  its  period,  about  2'^  12". 

These  two  examples  of  the  class  of  variable  stare  give  a 
rough  idea  of  the  extraordinary  nature  of  the  phenomena 
they  present.  A  closer  examination  of  othere  discloses 
minor  variations  of  great  complexity  and  apparently  with- 
out law. 

The  following  are  some  of  the  more  prominent  vari- 
able stare  visible  to  the  naked  eye : 


Nami. 


fi  PerMl.. . 
d  Cephei. . 
ti  Aqaihe.. 
fl  hjm . . . 
a  Herealiii. 

o  Ceti 

V  Hjdne.. 
n  ArguB.. 


2.4. 

l«v. 

A. 

m. 

«. 

3 

S9 

48 

22 

84 

21 

19 

4S 

01 

18 

46 

17 

17 

8 

49 

2 

12 

47 

18 

22 

87 

10 

40 

2 

Decllmtlon, 
18W. 


+  10 
4-67 
+  0 
+  88 
+  14 
-  8 
-28 


27-2 
40U 
40-4 
127 
82-4 
84-1 
8«-4 
01 


Period. 


(f. 

2M 
6M 
717 
12-91 
88-0 
8800 
4880 
70ye«n. 


ChMRM  of 

IfNpiltada. 


ST 

8-7 
80 

8i 
8  1 
2 

4 
1 


to 
4 

4-8 
4-7 

*k 

8-9 
10 
10 

6 


About  90  variable  stare  are  well  known,  and  as  many 
more  are  suspected  to  vary.  In  nearly  all  oases  the  mean 
period  can  be  fairly  well  determined,  though  anoirtalies  of 
various  kinds  frequently  appear.  Th«  principal  anomalies 
are : 

^ir«t.  The  period  is  seldom  constant.  For  some  stare 
the  changes  of  the  period  seem  to  follow  a  regular  law ; 
for  othere  no  law  can  be  fixed. 

Second.  The  time  from  a  minimnm  to  the  next  maxi- 
mum is  usually  shorter  thaa  from  this  maximum  to  the 
next  minimum. 

Third.  Some  stan  (as  fi  L^ra^  have  not  onlyone  max- 
imum between  two  consecutive  principal  minima,  but 
two  such  maxima.  For  /9  Zyroi,  according  to  Aboklam- 
DSK,  S'  9h  after  the  principal  minimnm  comes  the  first 
maximnti^  ;  titon,  8*  7^  after  this,  aaeeondary  minimum  in 
which  ^  itar  is  l^  no  means  so  funt  as  in  the  principal 


-I—    -,  .|iij>««iiiu.   I   i»n,m"^-U'»'      "WMiJ.i|»Ului..ti»JlllilLil.JBIU   - 


442 


ASTRONOMY. 


ininimuiii,  and  finally  3"*  3^  afterward  comes  the  principal 
maximum,  the  whole  period  being  12*'  21"  47'".  The 
courae  of  one  period  is  illustrated  below,  supposing  the 
period  to  begin  at  O'  0**,  and  opposite  each  phase  is  given 
the  intensity  of  light  in  terms  of  y  Ltfra  =  1,  according 
to  photometric  measures  by  Klein. 


PhMe. 

RotaMve 
Intamltjr. 

Prineljwl  Minimum 

Fint  Maximam 

0* 

8< 

0^ 

28" 

0-40 
0-88 

Second  MIntmnm 

Prindpftl  Maxlmani 

Prlncl|Mtl  Minimum 

6* 

IH 

la* 

008 
0-88 
0-40 

11  IS  I 


The  periods  of  94  we1Udet«nnined  variable  stars  being 
tabulated,  it  appears  tliat  they  are  as  follows  : 


PUtodbetwMn 

No.  of  SUn. 

Period  iMtwMn 

No.  of  sum. 

Id.  and    80 d. 
80               80 
80            100 
100            180 
180            800 
MO            800 
NO            800 
800            800 

18 

1 
4 
4 
5 
9 
14 
18 

800  d.  and  400  d. 
400             480 
480             800 
800             880 
880            800 
800            800 
680             700 
700            780 

18 
8 
8 

0 
0 

1 
0 

1 

Z=»4 

It  is  natural  that  there  should  be  few  known  variables 
of  periods  of  600  days  and  over,  but  it  is  not  a  little  re- 
markable that  the  periods  of  over  half  of  these  variables 
should  fall  between  250  and  450  days. 

The  color  of  over  80  per  cent  of  the  variable  stan  is  red 
or  orange.  Red  stars  (of  which  600  to  700  are  known) 
are  now  receiving  close  attention,  as  there  is  a  strong  like- 
lihood of  finding  among  them  many  new  variables. 

The  speokra  of  variable  stars  show  ohangoo  which  ap- 
pear to  be  oonneoted  with  the  variations  in  th«lr  li||^t. 


66  the  principal 

21"  47'".      Tiie 

,  Buppoeing  the 

ti  phftfie  ia  given 

=  1,  according 


RoteMve 

IntMMitjr. 

0*      0» 

0-40 

8*      » 

0-88 

6*      »» 

0-58 

JH    12" 

0-88 

8*    82- 

0-40 

iable  8 

tars  being 

W8  : 

ram 

Mo.  of  Stan. 

100  d. 

18 

iSO 

8 

MM 

(50 

00 

00 

W) 

m 

Xz=9A 

known  variables 
is  not  a  little  re- 
)f  these  variables 

riable  stars  is  red 
700  are  known) 
9  is  a  strong  like- 
variables. 
laqgM  which  ap- 
in  tiMir  lifi^t. 


443 


TBMPORARY  STARS. 


Another  clau  of  variatioM  oooun  awoag  th«  fixed  atan — naaMly, 
Tariatiooa  in  color,  «ith«r  with  or  without  oomaponding  chaogea 
of  maffnitude. 

In  tne  Urmtomitry,  compoaed  in  the  middle  of  the  tenth  century 
bv  the  Peraian  aatronomer  Al  Bdri,  it  ia  atated.  that  at  the  time  of 
hia  obiervaticma  the  star  Algol  waa  reddiali — a  term  which  he  ap- 
pliea  alio  to  the  itais  Antaru,  AUUbartm,  and  some  others.  Most 
of  these  still  exhibit  a  reddish  aapect  But  AIm^I  now  aupeara  aa  a 
white  star,  without  any  sign  of  color.  Dr.  Klbiii,  of  Cologne, 
discorered  that  a  Vrta  ikuorU  periodically  changes  color  from  an 
intense  fiery  red  to  a  yellow  or  Tellowlah-red  every  five  weeka. 
Wbbkr,  of  Peckeloh,  has  obaenrea  this  atar  lately,  and  finds  thia 
period  to  be  well  establiahed. 

%  S.    TXMPOBABT  QB  HSW  STABS. 

There  are  a  few  oases  Icnown  of  apparent!;^  new  stars 
which  have  suddenly  appeared,  attained  more  or  less 
brightness,  and  slowly  decreased  in  magnitude,  either  dis- 
appearing totally,  or  finally  remaining  as  comparatively 
faint  objects. 

The  most  famous  one  was  that  of  1672,  which  attained 
a  brightness  greater  than  that  of  Siriua  or  Jupiter  and 
approached  to  Fmiim,  being  even  visible  to  the  eye  in 
daylight.  Ttoho  Bbahk  first  observed  this  star  in  No- 
vember, 1573,  and  watched  its  gradual  increase  in  light 
until  its  maximum  in  December.  It  then  began  to  diminish 
in  brightness,  and  in  January,  1578,  it  was  fainter  than 
JupU«r.  In  February  and  iLuvh  it  was  of  the  1st  mag- 
nitude, in  April  and  May  of  the  3d,  in  July  and  August  of 
the  3d,  and  in  October  and  November  of  the  4th.  It  con- 
tinued to  dimihish  until  March,  1574,  when  it  became  in- 
visible, an  tiie  telescope  was  not  then  in  use.  Ito  color, 
at  first  intense  white,  decreased  through  yellow  and  red. 
When  it  arrived  at  tiie  5th  magnitude  its  color  again 
became  white,  and  so  remained  till  its  cBsippearanoe. 
Ttoho  measured  it/^distance  carefully  from  nine  stan  near 
it,  and  near  it<;  phM)e  there  is  now  a  star  of  the  10th 
or  11th  magnitude,  which  is  possibly  the  same  star. 

The  histcuy  ^t  temporary  stars  is  in  gmeral  similar  to 
that  oi  the  star  of  1573,  except  th&t  oon«  have  ftttainied  so 


444 


ASTHONOifT. 


groat  a  (logrcx)  of  *;ii  <Mi<i/,  Moru  ^liaii  a  avoro  of  Mioh 
objects  are  known  i.o  ;;  o  i.^ptTocI,  many  of  them  before 
the  making  of  accurate  obtM^rvations,  and  the  conclusion  ia 
probable  that  many  have  appc  ired  without  recognition. 
Among  telescopic  Btars,  there  is  but  a  amall  chance  of  de- 
tecting a  new  or  temporary  star. 

Several  supposed  cases  of  the  disappearance  of  stars  ex- 
ist, but  here  there  are  so  many  jiossible  sources  of  error 
that  great  caution  is  necessary  in  admitting  them. 

Two  temporary  stars  have  appeared  since  the  invention 
of  the  speutroscoiw  (1850),  and  the  conclusions  drawn 
from  a  study  of  their  spectra  are  most  important  as  throw- 
ing light  upon  the  phenomena  of  variable  stars  in  general. 

The  iirst  of  these  stars  is  that  of  1866,  called  T  Coronat. 
It  was  first  seen  on  the  12th  of  May,  1866,  and  was  then 
of  the  2d  magnitude.  Its  changes  were  followed  by  vari- 
ous observers,  and  its  magnitude  found  to  diminish  as 
follows  : 


MM  * 

Mm  12 8- 

10. 


14. 
15. 
16. 
17. 


May  18 8-8 

"•0 
•5 
•0 
•S 
•0 


10. 

w. 

81. 
88. 
88. 


«• 
6- 
7- 
7- 
8- 


By  June  7th  it  liad  fallen  to  9—0,  and  July  7th  it  was 
9" -5.  SoHMnrr's  observations  of  this  star  {T  CcTanci)y 
continued  up  to  1877,  show  that,  after  falling  from  the 
second  to  the  seventh  magnitude  in  nine  dayi,  its  light 
diminished  very  gradually  year  after  year  down  to  nearly 
the  tenth  magnitude,  at  which  it  has  remained  pretty  con- 
stant for  some  yean.  Butduring  the  whole  period  there 
have  been  fluctuations  of  brightness  at  tolerably  regnhv 
intervals  of  ninety-four  days,  though  of  sncoessiyely  de- 
creasing extent.  After  the  first  sudden  fall,  there  seems 
.to  have  been  an  increase  of  brilliancy,  whidi  brought  the 
star  above  the  seventh  magnitude  again,  in  October, 
1866,  an  increase  of  a  full  magnitude ;  bntrinee  that  time 


■iif.!^iSaM|U«lS 


a  iM.'oro  of  Biioh 
of  them  before 
ho  conduBion  ia 
lut  reoognition. 
11  chance  of  de- 

,nce  of  Btan  ex- 
ources  of  error 
I  them. 

le  the  invention 
icluaions  drawn 
artant  as  throw- 
Btans  in  general. 
Hod  T  Corona. 
3,  and  was  then 
>Uowed  by  vari- 
to  diminish  as 


5-5 

«0 

6-6 

7-0 

7.B 

80 

July  7th  it  was 
ar  {TCoron(B\ 
dling  from  the 
dayi,  its  light 
down  to  nearly 
ined  pretty  oon- 
ole  period  there 
Dlerably  regnliMr 
SQOoessively  de> 
all,  there  seems 
dch  brought  the 
n,  in  October, 
trince  that  time 


YARIAHLK  STARS. 


445 


tho  cluitigoM  liavo  boon  niiiuh  smaller,  ntul  aru  now  but 
littlo  mora  than  a  tenth  of  a  magnitude.  Tho  uolor  ot  the 
Btar  has  been  pale  yellow  throughout  tho  whole  course 
of  observations. 

The  ■pectroKopic  obMrrstions  of  this  iitsr  by  HnnutNS  and 
MiLLBR  inowed  it  to  har«  »  speotrom  then  abaolutely  unique.  The 
report  of  their  obserrationB  sayi,  "  the  Mpectruni  of  thia  object  ia 
twofold,  showing  that  the  lioht  by  which  it  ihineB  hM  emankted 
from  two  dietinct  sources.  The  principal  spectrum  is  usIobous 
to  that  of  the  sun,  and  is  formed  of  light  which  wu  emitted  by 
■n  incandescent  solid  or  liquid  photosphere,  and  which  has  suffered 
a  partial  absorption  by  passing  through  an  atmosphere  of  vapors  at 
a  lower  temperature  than  the  photosphere.  Buperpoeed  over  this 
spectrum  is  a  second  spectrum  consisting  of  a  few  hight  lines 
which  is  due  to  light  which  has  emanated  from  intensely  heated 
matter  ia  Uie  state  of  gas." 

In  November,  1876,  Dr.  Schmidt  discovered  a  new  star  in  Gyg- 
ntM,  whose  telescopic  history  Ih  nimilar  to  that  given  for  T  Corona. 
When  discovered  it  was  of  tho  M  magnitude,  and  it  fell  rapidly 
below  visibility  to  the  naked  eye. 

This  new  star  in  Oygnua  war.  observed  by  Gobbc,  Copblajid,  and 
VoQBL,  by  means  of  the  spectroscope  ;  and  from  all  the  observa- 
tions it  is  plain  that  the  hydrogen  lines,  at  first  prominent,  have 
gradually  faded.  With  the  decrease  in  their  brilliancy,  a  lioe 
corresponding  in  position  with  the  brightest  of  the  lines  of  a  nebu- 
la has  strengtiwned.  On  December  8th,  t876,  this  last  line  was  much 
fainter  than  F  (hydrogen  line  in  the  solar  spectrum),  while  on 
March  9d,  1877,  F  was  vary  much  the  fsinter  of  tiie  two. 

At  flnt  it  exhibited  a  oontinuous  spectrum  with  numerous  bright 
lines,  but  in  the  latter  part  of  1877  ft  emitted  only  munochiomatio 
light  the  spsotrum  ooudsting  of  a  single  bright  line,  correspond- 
ing m  poduOTi  to  the  obaraoteriatio  line  of  gaseous  nebulc.  The 
intermediate  stages  wen  eharaeteriied  by  a  gradual  fading  out, 
not  only  of  the  continuous  spectrum,  but  also  of  the  bright  lines 
which  orossed  it.  From  this  fact,  it  is  inferred  that  this  star,  which 
has  now  fallen  to  10-S  magnitude,  has  actually  become  a  planetary 
nebula,  affording  an  instance  of  a  remarkabla  nversal  ot  the  pro- 
cess ima^^joMd  by  La  Piju»  in  his  nebular  theory. 


S  8.   CTSOBUB  of  VABIABLI  8TAB8. 

The  theory  of  variable  utars  now  generally  aooepted  by  investi- 
gators is  founded  on  the  following  Benenl  oonohisions  : 

(1)  That  the  only  distinction  wmoh  can  be  made  between  the 
various  classes  of  stars  we  have  just  desoribed  is  one  of  degree. 
Between  stars  as  r^pilar  as  AlgU,  whiek  goes  throuj^  its  period  in 
less  than  three  days,  and  the  suddsa  uashig  out  of  the  star  de- 


tli 

m 


'fi;bl'i 


446 


ABTHONOMT. 


scribed  by  Ttcbo  Brahb,  there  is  every  gradstion  of  irresnlarity. 
The  only  distinction  that  can  be  drawn  between  them  is  in  the 
length  of  the  period  and  the  extent  and  regularity  of  the  changes. 
All  sooh  stars  must,  therefore,  for  the  present,  be  included  in  the 
sixffile  class  of  variables. 

tt  was  at  one  time  supposed  that  newly  created  stars  appeared 
from  time  to  time,  and  that  old  ones  sometimes  disappeared  from 
view.  But  it  is  now  considered  that  there  is  no  well-established 
eaK  either  of  the  disappearance  of  an  old  star  or  the  creation  of  a 
new  one.  The  suppmed  cases  of  disappearance  aroee  from  catar- 
loffuen  accidentally  recording  stars  in  positions  where  none  existed. 
BwMequent  astronomers  flnfing  no  stars  in  the  place  concluded 
that  the  star  had  vanished  when  in  reality  it  had  never  existed. 
The  view  that  temporary  stars  are  new  creations  is  diqirwed  by 
the  ra|ddity  with  which  they  always  fade  away  again. 

(S)  That  all  stars  may  be  to  a  greater  or  lew  extent  variable ; 

ly  in  a  vast  majority  of  cases  the  variations  are  so  slight  as  to  be 
imperceptible  to  the  eye.  If  our  sun  could  be  viewed  from  the  dis- 
tance of  a  star,  or  if  we  could  actually  measure  the  amount  of  Hght 
which  it  transmits  to  our  eyes,  there  is  little  doubt  that  we  should 
find  it  to  vary  with  the  presence  or  absence  of  spots  on  its  surface. 
We  are  therefore  led  to  the  result  that  variability  of  light  may  be  a 
oommon  characteristic  of  stars,  and  if  so  we  are  to  look  for  its 
oauae  in  something  common  to  all  such  objects. 

Thb  spots  on  the  sun  may  give  us  a  hint  of  the  probable  cwase  of 
the  variations  in  the  light  of  the  stars.  The  general  analogies  of  the 
universe,  and  the  observations  with  the  spectroscope,  all  lead  as  to 
the  conclusion  that  the  phyrical  constitution  of  the  sun  and  stars  is 
of  the  same  general  nature.  As  we  see  spots  on  the  sun  which  varv 
in  form,  size  and  number  from  day  to  day,  w>  if  we  could  take  •  suf- 
Iciently  close  view  of  t^e  faces  of  the  start  we  should  probably  see 
^ota  on  a  great  number  of  them.  In  our  ann  the  apots  never  cover 
more  than  a  very  small  fraction  of  the  surface ;  Vut  we  have  no 
reason  to  suppose  that  this  would  be  die  ease  with  the  stan.  If 
the  spots  oarnnA  a  large  portion  of  the  sorfaoe  of  th«  star,  ttten 
their  varisitioBa  in  number  anJ  extent  wooli  cause  the  star  to  vary 
inlk^t. 

Tms  view  does  sJK,  however,  aooount  for  those  cases  in  which  ths 
light  of  a  star  is  suddenly  incnased  in  smount  hundreds  of 
B|it  tiw  speetanscrale  observattons  of  T  Oortim  dwi 
am^Mor  with  «»p««noBs  going  on  in  our  sun.  Mr.  Hmwnn's  ob- 
servamms,  wUoh  we  have  already  dted,  seem  to  show  that  thsre 
was  a  sadden  and  extraordinarr  ontburst  of  glowing  hydrogen 
fjrom  the  star,  which  by  its  owaliight,  aa  v  «U  as  by  heMog  np  the 
whole  sorfaoe  of  the  star,  eaased  an  increase  in  its  brilliancy. 

Now,  we  have  on  a  vary  small  scale  sosaething  of  this  aawe  kind 
going  on  in  oor  snn.  The  red  flamaa  which  are  ssea  during  a 
total  eclipse  are  caused  by  eruptions  of  hydrogen  from  the  farteror 
of  ths  sua,  aad  these  eraptioas  are  gSMraUy  eoaaected  with  the 
fasaki  or  portkma  wf  the  son's  dkk  nKNW  briUiank  than  tb 


I  the  lost  of 


^mmmmmmmmM^jf^-^ 


tn  of  irresalarity. 

n  them  is  in  the 

r  of  the  changes. 

included  in  the 

d  stars  appeared 
liaappearea  from 
>  well-established 
the  creation  of  a 

arose  from  cata- 
lere  none  existed. 

plaee  concluded 
Id  uerer  existed. 
I  is  disprored  by 
i;ain. 

extent  Tariable ; 
so  slight  as  to  be 
ired  from  the  dis- 
e  amount  of  Hght 
bt  that  we  shoinld 
Its  on  its  surface, 
of  tight  may  be  a 
t  to  look  for  its 

probable  caiase  of 
I  analogies  of  the 
[»pe,  all  lead  ns  to 
le  sun  and  stars  b 
he  sun  which  Tanr 
I  could  talce  a  suf- 
iwdd  probably  sea 
■pots  never  eoTer 
Vutwe  have  no 
ith  the  Stan.  If 
of  Oe  iter,  then 
le  the  star  to  vaiy 

Bases  in  which  the 
ladreda  of 
MS  show 
If.  HiNMiin'a  ob- 

0  show  tiiat  tlMie 
llowing  hydrogw 
liy  helping  up  the 
s  brilliantiy. 

(rf  this  saue  kind 
ire  seen  dnrlaga 

1  from  the  iittarbr 
mMMsted  wtth  the 
It  than  th«  feat  of 


VARIABLE  STABS. 


447 


The  general  theory  of  variable  stars  which  has  now  the  most 
evidence  in  its  favor  is  this  :  These  bodies  are,  from  some  general 
cause  not  fully  understood,  subject  to  eruptions  of  slowing  hydro- 
gen gas  from  their  interior,  and  to  the  f mrmation  of  dark  spots  on 
their  surfaces.  These  eruptions  and  formations  have  in  most  casra 
a  greater  or  less  tendency  to  a  regular  period. 

In  the  case  of  our  sun,  the  period  is  11  years,  but  in  the  case  of 
many  of  the  stars  it  is  much  shorter.  Ordinarily,  as  in  the  case  of 
the  sun  and  of  a  large  majwity  of  the  stars,  the  variations  are  too 
slight  to  affect  the  total  quantity  of  light  to  any  visible  extent. 
But  in  the  case  of  the  variable  stars  this  spot-producing  power  and 
the  liability  to  eruptions  are  very  much  sireater  than  in  the  case  of 
our  sun,  and  thus  we  have  chaoses  of  light  which  can  be  readily 
perceived  by  the  eye.  Some  adutional  strength  is  given  to  this 
theory  by  the  fact  just  mentioned,  that  so  lan^e  •  proportion  of 
the  variabh)  stars  are  red.  It  is  well  known  that  glowing  bodies 
emit  a  laroer  proportion  of  red  rays  and  a  smaller  proportion  of 
blue  ones  the  cooler  they  become.  It  is  therefore  probable  that 
the  red  atan  have  the  leasi  heat  This  being  the  case,  it  is  more 
easy  to  {voduoe  spots  on  their  surface ;  and  if  their  outside  surface 
is  so  cool  as  to  oeoome  solid,  tHe  glowing  hydrogen  from  the  in- 
terior when  it  did  burst  through  would  do  so  with  mora  pown 
than  if  the  surrounding  shell  wtte  liauid  or  gaseous. 

Thera  is,  however,  one  star  of  #hum  the  variations  may  be  due  to 
an  mUMj  diffefent  canse-^namely,  Aifol.  The  extreme  jegularity 
with  which  the  ligfat  of  this  object  fades  away  snd  disappears  siw- 
gesta  the  poasibimy  that  a  dark  body  may  be  revolving  around  it, 
and  partially  eclinttag  it  at  every  revohition.  The  law  of  variation 
of  ita  li|riit  it  so  &leient  from  that  of  the  light  of  other  variable 
Stan  as  to  soggnfe  a  diflarcnt  catise.  Most  othen  an  nefur  their 
m>«iiniim  fot  osly  a  anall  Mrt  <rf  thdr  period,  while  iij;^  is  at  its 
mitTimiiin  for  nine  tenths  el  it  Othen  an  subject  to  neariv  con- 
tinuona  ehauna,  iMi»  tha  light  of  Aiftl  remains  constant  during 
nine  tenths  o?  ita  period. 


CHAPTER  III. 


MULTIPLE    STARS. 

§  1.    GHABAOTBB    OF    DOUBIiE    AND    MXJVSIPLE 

BTABS. 

When  we  examine  the  heavens  with  telescopes,  we  find 
many  cases  in  which  two  or  more  stars  are  extremely  close 
together,  so  as  to  form  a  pair,  a  triplet,  or  a  group.  It  is 
evident  that  there  are  two  ways  to  account  for  this  ap- 
pearance. 

1.  We  may  suppose  that  the  stars  happen  to  lie  nearly 
in  the  same' straight  line  from  us,  hut  have  no  connection 
with  ea<di  other.  It  is  evident  that  in  this  case  a  pair  of 
stars  might  appear  double,  although  the  one  was  hundreds 
or  thousands  of  times  farther  off  than  the  other.  It  is, 
moreover,  impoBsible,  from  mere  inspection,  to  determine 
which  is  the  farther. 

2.  We  may  suppose  that  the  stars  are  really  as  near 
together  as  they  appear,  and  are  to  be  considered  as  form- 
ing a  connected  pair  or  group. 

A.  couple  of  stars  in  the  first  case  are  said  to  be  optically 
dotMe,  and  are  not  generally  classed  by  astronomers  as 
double  stars. 

Stars  which  are  considered  as  really  double  are  those 
which  are  so  near  together  that  we  are  justified  in  consider- 
ing them  as  physically  connected.  Such  stare  are  iaid  to 
be  phyiicaU/y  doiMey  and  are  generally  designated  as 
double  stars  simply. 

Though  it  is  impossible  by  mere  inspection  to  decide  to 
which  class  a  pur  of  stara  should  be  considered  as  belong- 
ing, yet  the  calculus  of  probabilities  will  enable  us  to  de* 


DOUBLE  STARS. 


440 


I    KUI/nFIiB 

loopes,  we  find 
ixtremely  close 
I  group.  It  is 
nt  for  this  ap- 

1  to  lie  nearly 
no  connection 
case  a  pair  of 
3  was  hundreds 
I  other.  It  is, 
n,  to  determine 

really  as  near 
dered  as  form- 
to  he  opUcaUy 
Eustronomers  as 

ahle  are  those 

ed  in  consider* 

ars  are  iaid  to 

designated  aa 


[>n  to  decide  to 
ired  as  belong- 
uble  OB  to  de- 


cide in  a  rough  way  whether  it  is  likely  that  two  stare  not 
physically  connected  should  appear  so  very  close  together 
as  most  of  the  double  stars  do.    This  question  was  first 
cQusidered  by  the  Rev.  John  Michell,  F.R.S.,  of  Eng- 
land, who  in  1777  published  a  paper  on  the  subject  in  the 
Philosophical  TramacHona.    He  showed  that  if  the  lucid 
stars  were  equally  distributed  over  the  celestial  sphere,  the 
chances  were  80  to  1  against  any  two  being  within  three 
miBtuies  of  each  other,  and  that  the  chances  were  600,000 
tol  against  the  six  visible  stars  of  the  Pleiades  being 
accidentally  associated  as  we  see  them.     When  the  mill- 
ions of  telescopic  stars  are  oonaidered,  there  is  a  greater 
probability  of  such  accidental  juxtaposition.     But  the 
probability  of  many  such  cases  ooourring  is  so  eztramely 
small  that  astronomers  regard  all  the  closest  paim  as  phy- 
sically connected.     It  is  now  known  that  of  the  600,000 
stars  of  the  finrt  ten  magnitudes,  at  least  10,000,  ot  one  out 
of  every  60,  has  a  oompani<m  within  a  disteAed  of  30'  of 
arc.    This  proportion  k  many  times  greater  than  could 
possibly  be  the  result  of  ulumee. 

There  are  several  eases  (rf  st«n  wbkth  appear  double  to 
the  nake4  e^'   Two  of  tlieae  ire  have  airaMlj  described 
—nameljr,  d  Tmiti  Mid  «  Lyn».    ITie  lattMr  k  a  most 
curious  and  InterMting  object,  from  the  liet  that  each  of| 
the  twoj^aniii^ii  tiompoae  it  k 
itHolf  donUe.    Jitll|»oraiiiikiag 
idea  of  4iie  p«W«#^^  the  tdae- 
cope  oaa -be   'formed-  tlmn    by 
pointing  a  poweiril  ir Aiment 
upon  this  obiect.    It  w^i'  then 
be  seen  that  wis  minute  y.ihv  oi 
points,  capable  of  i^ing  ^JLJa- 
gnished  only  by  the  mcM  t  pen^t 

eye,  k  really  oompovd  of  two  tJT  l».-ra»  qvAimorLV 
pain  of  stirs  wide    ^  uf  ,  with  a  '^^  '  ^^*^ 

group  of  smaller  st&n  Letwaen  4ind  s/onnd  them.  The 
figure  shows  the  appearanoe  in  a  tel«n<jcp<i  of  oondderable 
power. 


. I *m.iM  -1 1  iji ^t.jfmj-v.ytum 


450 


AaTRONOMT. 


BvrrtutioiiB  of  Doubto  Btem— Bbuuy  Byitanu.—  The 
most  intereeting  questioa  suggested  by  double  stara  is  that 
of  their  relative  motion.  It  is  evident  that  if  these 
bodies  are  endowed  with  the  property  of  mutual  gravita- 
tion,  they  must  be  revolving  around  each  other,  as  the 
earth  and  phuiets  revolve  around  the  sun,  e]tie  they  would 
be  drawn  together  as  a  single  star.  With  a  iew  of  detect- 
ing this  revolution,  astronomers  measure  .he  jfOtUion- 
mgUy  and  dutanoe  of  these  objecta.    The  diOance  of  the 


v^iti 


ov  i*oiinBV-*Ams> 


ponents  of  the  double  star  is  simply  the  apparent 

whieh  separates  them,  as  seen  by  tiie  observer.    It  is 

always  expraeiied  in  seconds  or  fractions  of  a  seccmd  of  arc. 

The  an^  of  •potiHAon^  or  "  position-angle"  as  it  isof  un 

called  for  brevity,  is  the  angle  which  the  line  joining  the 

two  (Mars  makes  with  the  line  drawn  ^m  the  brightest  star 

to  the  north  pole.     If  Uio  fainter  star  is  directiy  north  of 

brighter  one,  this  angle  is  xero ;  if  east,  it  is  90**;  if  southi 


Syitenui.—  The 
uble  Stan  is  that 
nt  that  if  these 

mutual  gravita- 
kch  oUier,  as  the 

e]«ie  they  would 

a '  lew  of  detect- 
«  .;he  jHmtion- 
«  diitanoe  of  the 


»Iy  the  apparent 
iieoheenrer.  It  is 
)f  a  seocmd  of  aro. 
igle"  as  it  isof  UTi 
eline  joining  the 
1  the  brightest  star 
direcdy  north  of 
,iti8  90<*;ifBOttth, 


DOUBLS  8TAR8. 


461 


it  is  180"  ;  if  west,  it  is  270°.  This  is  illnstrated  by  the 
figure,  which  is  supposed  to  represent  the  field  of  view  of 
an  inverting  telescope  pointed  toward  ^e  south.  The 
arrow  shows  the  direction  of  the  apparent  diurnal  motion. 
The  telescope  is  supposed  to  be  so  pointed  that  the  brighter 
star  may  be  in  the  centra  of  the  field.  The  numbers 
around  the  surroimding  drde  then  show  the  an^e  of  po- 
sition, supposing  the  smaller  star  to  be  in  the  direetitm  of 
the  number. 

The  letters  »n.,  »f^  np,  and  nf  r>how  the  methocb  of 
dividing  tiie  four  quadrants,  <  meantug  souUi,  n  north, 
/  following,  and  j»  preceding.  Tha  two  lattw  words  refer 
to  the  direction  of  the  diur- 
nal motion.  Fig.  184  is  an 
example  of  a  pair  of  stars  in 
which  the  position-angle  is 
about  44°. 

If,  by  measures  of  this 
sort  extending  through  a 
series  of  yean,  the  distaUM 
or  poritiou-angle  of  a  pair 
of  stars  is  found  to  clun^ 
it  shows  that  one  stw  is  re- 
volirii^  around  the  other. 
Such  a  pair  is  called  a 
hmary  ttar  or  hinaty  «y»~ 
tern.  The  only  diatiaeliott 
whidi  we  can  make  between 
binary  qrstems  and  ordinary  donbk  staas  is  founded  on 
the  presence  or  absence  of  obaerred  motion.  It  is  prob- 
able tibat  nearly  all  the  douUe  stan»«are  really  binary  sys- 
tems, but  that  many  thousands  of  years  we  required  to 
perform  a  revolution,  so  that  tiie  molion  has  not  yet  been 
detected. 

The  disnoveiry  of  Unary  systems  is  one  of  great  sden- 
tiflc  ittterebt,  because  from  them  we  learn  that  the  law  ot 
gravitati<m  iaQhulee  the  stan  as  well  as  tSw  solar  system  in 


nOlpUl  STAlk 


453 


A8TR0N0MT. 


its  scope,  and  may  therefore  bo  regarded  as  a  universal 
property  of  matter. 

Oolora  of  Double  Stan.— There  are  a  few  notewortliy  statistics 
in  reoard  to  the  colors  of  the  coimmnents  of  double  stars  which 
may  oe  j^ven.  Among  596  of  the  orighter  double  stars,  there  are 
875  pairs  where  each  component  has  the  same  color  and  intensity  ; 
101  pairs  whore  the  components  have  same  color,  but  different  in- 
tensity ;  130  pairs  of  different  colofs.  Among  those  of  the  same 
color,  the  vast  majority  were  both  white.  Of  the  476  stars  of  the 
same  color,  there  were  295  pairs  whose  components  were  both 
white  ;  118  pairs  whose  components  were  both  yellow  or  both  red  ; 
68  pairs  whose  components  were  both  bluish.    When  the  com- 

Eonents  are  of  different  colors,  the  .brighter  generally  appears  to 
ave  a  tinge  of  red  or  yellow ;  the  other  of  blue  or  green. 

These  cbita  indicate  in  part  real  physical  laws.  They  also  are 
partly  due  to  the  physiological  fact  that  the  fainter  a  star  is, the 
more  bloe  it  'vill  appear  to  the  eye. 

MMMmsas  of  Pottbto  Mun.— Tlie  first  systematic  measures  of 
the  relative  poritiMi>  of  tlia  oaalponents  of  double  stars  were  made 
by  OwKOHUX  MAnn,  IMreotw  of  the  Ducv.  Observatory  of  Mann- 
heim. 1739,  hut  it  is  to  8m  WriJJAX  HuucHBLthat  we  owe  the  ba- 
,  sis  of  ear  kiiowtodfe  «>f  tUsbtaach  of  sidereal  astronomy.  In  1780 
HBMpBBcaMamred  1^  r«latlv«  situation  of  more  than  400  double 
Stan,  and  after  repeating  kia  measures  smne  score  of  years  later, 
ke  fooad  in  aboat  SO  of  the  peirs  evidence  of  relative  motion  of 
theoofispoMnts.  la  thia  Inat  mirvey  he  foimd  97  stars  whose  dis- 
taaoe  was  ooder  4',  IM  iMftireen  4'  and  8',  114  between  8'  and 
16',  aod  1«2  between  W  tuA  W. 


8iMw  }Ii&aaoau.'a  obeervaliooa,  the  discoveries  of  Bir  Joan  Hbb- 
.  temvu,  Sir  iiMm  Boom,  Dawm,  and  many  others  in  England,  of 
W.  Snuvii, '  Ono.  Bnora,  Kadlbb,  SUccbi,  Dbmbowski,  Dd- 
muif  ia  larope,  bm  of  G.  P.  Bono,  Alvam  Olabk,  and  8.  W. 
lUttn^  ia  tM  Vaitod  States,  have  increased  the  number  of 
kBowa  dooUa  ataia  to  aboat  1«»000. 

fiiesides  the  doable  stars,  there  are  also  triple,  quadruple,  etc., 
-ftuA  '  TiMe  aw  geBeriioany  called  imd^pb  Kara.  The  most  re- 
markable multiple  star  is  the  Trapmmm,  in  the  c^tre  of  the  nebula 
of  Orion,  comnionly  called  0  OriSiii$^  whose  ftmr  stars  are,  without 
doubt,  physically  conneeted. 

Th^  next  combibatioa  beyond  a  multiide  star  is  a  (dwiter  of  stars ; 
and  beginidng  with  clusters  of  T  in  diameter,  such  objeefes  may  be 
found  up  to  80'  or  more  in  diameter,  every  intermediate  siae  being 
represented.    These  we  shall  consider  shortly. 

%  t.    OBBm  or  BINABT  STAB8. 

When  it  was  established  that  many  of  the  doiible  stars  were  really 
revolving  around  each  otner,  tt  iiecaine  of  great  interest  to 
detenaiae  tiie  orbit  aud  aaoMrlaIn  whether  it  wA  an  ellipse,  with 


as  a  uni  venal 


tewortliy  statiatica 
louble  stars  which 
ble  stars,  there  are 
lor  and  intensitv ; 
,  but  different  m- 
those  of  the  same 
lie  476  stars  of  the 
inents  were  both 
bIIow  or  both  red  ; 
When  the  com- 
nenUly  appears  to 

or  green. 

>.  They  also  are 
dnter  a  star  is,  the 

matic  measures  of 
le  stars  were  made 
erratoryof  Mann- 
lat  we  owe  the  ba- 
tronomy.  In  1780 
« than  400  double 
K>re  of  years  later, 
relative  motion  of 
n  stars  whose  dis- 
between  8'  and 

I  of  Bir  Jobs  Hbb- 
)n  in  England,  of 
DbmbOwski,  Dn- 
Ilabk,  and  B.  W. 
id  the  number  of 

e,  quadruple,  etc., 

r$.    The  most  re- 

mtre  of  the  nebula 

stars  are,  without 

taaluaterof  Stan; 
ich  objeeta  may  be 
nediate  siae  being 


ABB. 

le  stars  were  really 
great  interest  to 
S  an  elUjMe,  with 


BINART  STARS. 


458 


the  centre  of  gravity  of  the  two  objects  in  one  of  the  foci ;  if  so,  it 
would  be  shown  that  gravitation  among  the  stars  followed  the  same 
law  as  in  the  solar  system.  As  an  illustration  of  how  this  may  be 
done,  we  present  the  following  measures  of  the  position-angle  and 
distance  of  the  binary  star  i  l^rtas  Majoria,  which  was  the  first  ane 
of  which  the  orbit  was  investigated.    The  following  notation  is 


used : 
star; 


the  angle  of  position;  $, 
the  fainter  one. 


the  distance ;  A,  the  brighter 


f  Ukbm  Majorib  =  1 1528.* 


Epoch. 

P 

(. 

Obwrrtr. 

17820 

1808-1 

148*8 

»7-6 

276-4 

264-7 

201-1 

150-0 

122-6 

96-7 

16-5 

• 
•  •  •  ■ 

1-00 
2-45 
2-90 
2-56 
001 

W.  HersclieL 

1820-1 

1821-8 

W.  Blruve. 

1881-8 

J.  Hersehel. 

1840-8 

1851-6 

1863-2  

Dawes. 
MKdler. 
Dembowskl. 

1872-5  

DnnCr. 

If  these  measures  be  plotted  on  a  sheet  of  squared  paper,  the 
several  positions  of  B  will  be  found  to  lie  in  an  ellipse.  Tais  ellipse 
is  the  projection  of  the  real  orbit  on  the  plane  perpendiculiur  to  the 
line  of  sight,  or  line  joining  the  earth  with  tiie  star  A.    It  is  a 

?|uestion  of  analysis  to  determine  the  true  orbit  from  tbo  times  and 
rom  the  values  of  p  and  j. 

If  the  real  orbit  m^pened  to  lie  in  a  pUme  perpendiwtfar  to  tlie 
line  of  8i|riit,  the  star  A  would  lie  in  the  fooua  of  the  eftipse.  If 
this  oolnddenee  does  not  take  place,  thenth«  plane  of  the  true  or- 
bit is  aeen  obliquely. 

IIm  flnt  two  of  KBPun's  laws  can  be  employud  in  determiaing 
such  oittta,  but  tiie  third  Uw  is  inapplicable. 

Ittnm  of  Bfaary  87>tainB.--WIien  the  panllaz  or  distance, 
the  soni-major  axis  St  the  orbit,  and  tiie  time  of  revolution  of  a 
bhiary  ^atem  are  known,  we  can  determine  tiie  oomUned  mass  of 
the  pair  of  atari  in  terms  of  tiie  nuas  of  the  son.    Let  us  put : 

4^  tlie  mean  distaaee  of  the  two  componeBta  aa  measMwd  in 
seconds; 

o,  tiieir  mean  distance  from  each  other  in  astrononik«l  units ; 

T,  ike  time  of  revolution  in  yean ; 

Jf,  Jf*.  the  msHes  of  the  two  coaponrat  stars ; 

P,  tiior  annual  parallax ; 

D,  tiieir  diatance  in  aatronomioal  unite. 

*  Z  1588  slgnUea  ikaX  this  star  la  No.  1AB8  of  W.  8im«»\i  Dorpat 
CatatoffttSi 


■^>:^- 


484 


ASTnONOMY. 


From  the  geneT»»«rtion  of  Kbplm's  third  l»w,  given  by  the 
theory  of  gravitation,  we  liave 

M*  +  M  =  "rpT' 

Fron  the  formole  expUlned  in  treating  of  parallax  we  have 

D  =  I  -*-  tin.  P. 

If  a'  ia  the  major  axie  In  aeconda.  a  being  the  aame  quantity  In 
aatronomical  unite,  then  ! 

a  =  D  ■  tin.  a". 


From  theoe  two  equations, 


tin.  a' 
tin.  F 


a' 
F 


becauM  o'  and  P  are  ao  amatl  tUt  the  ares  may  be  tetcen  for  their 

Putting  this  value  of  a  In  the  equation  for  Jf  '  ■  Jf«> 
we  liave  M  +  M»  =  ^j"  p»' 

have  been  determined  (O'BS  and  0'  16)  from  direct  meaanrea.    For 
T  =  770  years;  a"  =  IS'-S  ;  P  =  0  -98 ; 

totpOphiwihi, 

r=  94-4  years;  a"  =  4"-70;  P  =  O'le. 

If  we  subeUtnte  in  the  last  equntion  these  values  for  T,  P,  and  a', 

VTA  llftTO 

jr.  4-  if  =  0«7  for  a  Centauri, 
jr.  ■•-  jr=  9-84  forp  OpMtuhl 

The  last  number  1»  quite  uncertain,  owing  to  the  diffloalty  of  mmMr 
aring  so  small  a  parallu.  We  c«i  only  eonelude  that  the  mass  of 
S  two  s*"^  not  many  times  greater  or  leat.tlum  the  my*  of 
onrmn.    Rom  the  agreement  in  these  two  eaae%  it  la  j^oMiletbiU 

"notC,^  if  i&n^  «mW  be  «>^"»»::;;  " 'St^ 
gtaatly  d*erent  flrom  the  mass  of  «jr  aw»  We  ^^^^J^V^' 
tion,  whiehammmts  to  supposing  JT.  +  Jr=  1,  •PI*/  »•  fcm«»» 

p  =  a'  f  ri 

to  other  biMtriea.  and  dednco  a  value  te  Pin  «?*  ••f^.^^S'*  ••.?H2? 
thehypothetloal  painllax  (Qyld«n),  and  which  to  probably  not  fte 

The»  are,  iMaide  binary  systems,  multipto  <»«>  aa  f  OwMrt.  y*ere 
the  distanoe  if  il  and  B  is  O'-S ;  and  fiom  the  ntld^  l»tot  between 

.1  and  B  to  <7to  5"5.    The  period  of  revolution  of  — jj—  rtewt  0  is 

supposed  to  be  about  TM  year..  W  >»  «»•  jl-J  ^"'^r  **"* 
r  =  780  year*  and  a"  =  6" -6,  we  have  the  hypothetleal  parallas 


BINAnr  BTAR8. 


m 


law,  giren  by  the 

mlUz  wfl  hftve 

the  Mme  quantity  in 


ay  be  Uken  for  Uiaijr 


Htan  wlioae  parallaxes 
direct  meaaarea.    For 

=  0'-98; 


=:0'16. 

kluea  for  T,  P,  and  a', 
vri, 

» tbe  difBoolty  of  maaa- 
ilade  that  the  maaa  of 
r  laaa  than  tha  aaaa  of 
Nik  it  la  pntaMatbat 
ilMd,  it  wottld  not  be 
I  Bay  OB  Mm  niMoai- 
,  apply  tha  fMnuh 

idtaaaawUehkeallai 
li  ia  pfobably  not  far 

maa  aa  C  Cbiwri,  whara 
Biiddle  point  bati»«eB 

,„C^.fca.l(7ia 

I  laat  fbrmnla  w«  pat 
otiMtleal  parallax 


Following  are  giTen  the  elemenU  of  several  of  the  more  impor* 
tif't  binary  etars.  Eight  of  these  have  moved  through  an  entire 
revolution — 860° — since  the  first  observation,  and  about  150  are 
known  which  have  certainly  moved  through  an  arc  of  over  10°  since 
they  were  first  obaerved. 

In  the  tablea  the  semi-major  axia,  or  mean  distance,  must  be 
given  in  seconds,  since  we  have  usually  no  data  by  which  ita  vain* 
in  linear  measurea  of  any  kind  can  be  fixed. 

Periods  of  revolution  exceeding  120  years  must  be  regarded  as 
quite  uncertain. 

ELmBNTa  or  Binary  fh'ABs. 


Stab's  Naim. 

Period 
lYewi.) 

43  ComeBer.... 

85-7 

(  Heroolla 

84  6 

X  818l» 

8708 

n  Corona  Bor. . . 

40-9 

S  Ubne 

9S.90 

y  Cofoue  Aas. . . 

05-5 

(  Vna  Maj. . .  | 

80-6 
808 

f  Cancri j 

684 
60S 

aCentaori 

850 

70Oiriiluefal 

92-8 

Y  GOKMUBBor.... 

son  Z 

955 

104-4 

u  Leonia 

il4-8 

AOphluohi 

883-8 

/>  Bridaal 

117-5 

1788  2 

184-5 

fBoMIs 

1274 

rOpfiiuehi 

1750 
817-9 

V  CaHlopee 

898-4 

44Bo(Rl8. 

88M 

1988  2 

^•Bofltla 

880-8 

88  Aadnmeda... 

849- 1 

Y  LeoBia 

408-8 

81  t^ifpii....... 

4IS1 
488-0 

«  Cow—  Bat.. . . 

84S-9 

a  QantaMfQBi... 

1001-8 

(Aqnarii......  . 

1018-8 

Time 
of  Peri- 
Mtron. 


1889-9 
1884-9 
1842-8 
1849-9 
1889-8 
1889-7 
1875.6 
1870-8 
1889-8 
1889.9 
1874-9 
1807-9 
1848-7 
1884-9 
1841-8 
1808-9 
1817-5 
1868-0 
1770-7 
1886-0 
1881-9 
1909-2 
1788-0 

1868-0 

1796-8 
1741-1 
18041 

1888-9 
17«l-8 
18841 


Seml- 

Azlt 

Major. 


0' 
1 

'S 

1 

8 
2 
2 
0 
0 
21 
4 
0 
1 
0 

1 

8 

4 
8 
1 
9 
8 

1 

1 
8 
2 
10 
0 
7 
7 


•60 

0- 

-86 

0^ 

-711 

0- 

•99 

0- 

-26 

0- 

-40 

0- 

-08 

0 

•04 

0- 

90 

0^ 

91 

0- 

•80 

0- 

•88 

0 

•70 

0 

-27 

0- 

-80 

0- 

-19 

0- 

-89 

0- 

«  •  • 

0- 

•86 

0- 

-89 

0^ 

-40 

0^ 

-88 

0- 

-08 

0- 

47 

0^ 

•54 

0- 

•00 

0- 

-81 

0- 

•4 

,  ^ 

•88 

0- 

•48 

0^ 

•64 

0^ 

Iceen- 
trieity. 


Oaleulstor. 


•48 
•41 
•86 
■29 
•08 
-69 
88 
•87 
•00 
-87 
-67 


-46 
-00 

•4a 

-88 
-66 

-71 
•87 
•61 
•07 
•71 

•60 

•60 

-74 


70 
•88 
•60 


Dabiago. 

Flammarion. 

Doberek. 

FlammarioB. 

Doberek. 

Sohiaparelll. 

Hind. 

Flammarion. 

O.  Strove. 

Flammarion. 

Hind. 

Flammarion. 

Doberek. 

Doberek. 

DoberdL 

Bohntk. 

Doberek.. 

Dobmek. 

Doberdt. 

Flammarion. 

DobaM*. 

DobevA. 

Dobank. 

Dobesek. 

Doberek. 
Doberek. 


Doberek. 
DobardL 
Doberek. 


•Slfi  S  algBMaBira  8181  oTW.  9niimii^i Dotpat Oatalogae. 


•V  •WKfft-,---;.!'  Mit'*  'airvM-r*.!^  ■ '— ■ 


466 


ABTRONOMT. 


The  flnt  computation  of  the  orbit  of  a  binary  atar  waa  made  by 
Savary  (Astronomer  at  the  Paris  Observatory)  about  1826,  and  his 
reaulU  were  the  first  which  demonstrated  that  the  laws  of  sravitu- 
tion,  which  we  knew  to  be  operative  over  the  extent  of  the  solar 
system,  and  even  over  the  vast  space  covered  by  the  orbit  of 
IIallby'i  comet,  extended  even  furtner,  to  the  fixed  stars.  It  might 
have  been  before  189fi  a  hazardous  extension  of  our  views  to  sup- 
pose even  the  near.dt  axed  stars  to  be  subject  to  the  laws  of  New- 
ton ;  but  as  many  of  M-'>  known  binaries  have  no  measurable  paral- 
lax, it  is  by  no  means  an  unsafe  conclusion  that  every  fixed  atar 
which  our  best  telescopes  will  show  is  subjected  to  the  same  laws 
as  those  which  govern  tin-  fall  of  bodies  upon  the  earth. 


■tar  WM  made  by 
iboiit  1826,  and  hU 
lie  law8  of  ffravitu- 
extent  of  the  solar 
1  by  the  orbit  of 
xod  stars.  It  might 
our  views  to  sup- 
9  the  laws  of  Nbw- 
)  measurable  paral- 
kt  every  flxca  star 
i  to  the  same  laws 
le  earth. 


CHAPTER    IV. 

NEBULuE  AND  CLUSTERS, 
g  1.    DISCOVERT  OF  NBBUUB. 

In  the  star-cat't^  'uea  of  Ptolkmv,  IlKVEUcg  and  the 
earlier  writors,  th  w  iuclnded  a  class  of  nebulous  or 

cloudy  stars,  whi(  o  in  reality  star-clusters.     They 

appeared  to  the  nu.  a  oyo  as  masses  of  soft  diffused  light 
of  greater  or  less  extent.  In  tliis  respect,  they  were  quite 
analogous  to  the  Milky  Way.  When  Galilbo  first  direct- 
ed his  telescope  to  the  sky,  the  nebulous  appearance  of 
these  spots  vanished,  and  they  were  seen  to  consist  of 
clusters  of  stara. 

As  the  telescope  was  improved,  great  numbers  of  such 
patches  of  light  were  found,  some  of  which  could  be  re- 
solved into  stare,  while  othera  could  not.  The  latter  were 
called  fiMtla  and  the  former  star-dwtera. 

About  1660,  HuYOHBNS  described  the  great  nebula  of 
Orion,  one  of  the  most  remarkable  and  brilliant  of  these 
objects.  During  the  last  century,  Mbssieb,  of  Paris,  made 
a  list  of  103  northern  nebulaa,  and  Laoaiixb  noted  a  few  of 
those  of  the  southern  sky.  The  careful  sweeps  of  the 
heavens  by  Sir  William  Hkbsobsl  with  his  great  tele- 
scopes first  gave  proof  of  the  enormous  number  of  these 
masses.  In  1786,  he  published  a  catalogue  of  one  thousand 
new  nebulffi  and  clusters.  This  was  followed  in  1789  by 
a  catalogue  of  a  second  thousand,  and  in  1802  by  a  third 
catalogue  of  five  hundred  new  objects  of  this  class.     A 


458 


ASTRONOHr, 


■iiiiilnr  serios  of  Hwoop,  carriod  on  hy  Sir  John  IIkr- 
twiiKL  ill  Ijoth  homiupliores,  added  about  two  thouBand 
more  nobulai.  The  i^euoral  catalogue  of  nobulto  and  cluu- 
tore  of  stare  of  the  latter  astronomer,  published  in  1864, 
contains  5079  nebulaj :  6261  arc  known  in  1879.  Over 
two  thirds  of  those  were  first  discovered  by  the  IIebschels. 
The  more  enumeration  of  over  4000  nobuluu  is,  how- 
ever, but  a  small  i>art  of  the  labor  done  by  these  two  dis- 
tinguished astronomers.  The  son  htis  left  a  great  number 
of  studios,  drawings,  and  measures  of  nebulw,  »i  '  the 
memoirs  of  the  father  on  the  Construction  of  the  Ilti  v  •  n 
owe  their  suggestiveness  and  much  of  their  value  to  Jiis 
long-continiiod  observations  on  this  class  of  objects,  which 
gave  him  the  clue  to  Ids  theories. 


%  a.  Oi:.AB8IFIOATIONOFKBBnLJIiLnT''aLn8TBB8. 

In  studying  these  objects,  the  flrst  question  wo  meet  is 
tliis :  Are  all  these  botiies  clusters  of  stars  wlii*;!*  look 
diffused  only  because  they  are  so  distant  that  ouv  twla- 
scopes  cannot  distinguish  them  separately  t  or  are  bovuc  .>f 
them  in  reality  wlwt  they  seem  to  be— namely,  difiosed 
massefl  of  matter  f 

In  his  early  memoirs  of  1784  and  1786,  Sir  William 
Hbbsohbl  took  the  first  view.  He  considered  the  Milky 
Way  as  nothing  but  a  congeries  of  stars,  and  all  nebnls 
naturally  seemed  to  him  to  be  but  stellar  dusters,  so 
distant  as  to  cause  the  indiridnal  stars  to  disappear  in  a 
general  milkiness  or  nebulosity. 

In  1791,  however,  his  views  underwent  a  change.  He 
had  discovered  a  nebulous  star  (properly  so  called),  or  a 
star  which  wa«  undoubtedly  similar  to  the  surrounding 
stars,  and  which  was  encompassed  by  a  hala  of  nebulous 
light.  * 

*  TlUa  was  the  6Mi  ndmla  of  bUfourtk  ebmat  pluietaiy  nebula. 
(B.  lT.«9.)  .  , 


Sir  John  IIkk- 
t  two  tliouiiand 
nobulso  and  cltui- 
ibHahodiu  1864, 
lit)  1879.  Over 
>y  the  IlERScnBLB. 

nubuliu  ia,  how- 
ty  those  two  dis- 
ft  a  great  number 
nubulte,  tfi  '  the 
mof  the  Ilti  V  -n 
heir  value  to  iii« 
of  objects,  which 


estiou  wo  meet  is 
stars  whi<:lt  look 
tit  that  otjv  'm\9- 
fi  or  are  bo!u(!  >f 
-namely,  difiosed 

r85,  SirWauAM 
sidered  the  Milky 
K,  and  ail  nebulse 
tellar  clnsters,  so 
to  disappear  in  a 

it  a  change.    He 

y  so  called),  or  a 

the  surrounding 

halo  of  nebulous 


of  ^snetaiy  nebola. 


^'°*^  'IWW 


^h^-- 


CIHM/ICMH 

Microfiche 

Series. 


CIHIVI/ICIVIH 
Collection  de 


Canadian 


Inatituta  for  HIatorlcal  MIcroraproductlona  /  Inathut  Canadian  da  microraproductiona  itiatoriquaa 


,aw«-i.taaiw.'iint 


NEBULA  AND  CLITSI'ERS. 


459 


lie  says  :  **  Nobulo;  can  be  selected  so  that  an  insensible  grada- 
tion shall  take  place  from  a  coarse  cluster  like  the  Pleiade*  down  to 
a  milky  nebulosity  like  that  in  Oritm,  every  intermediate  step  being 
represented.  This  tends  to  confirm  the  hypothesis  that  all  are  com- 
ftosed  of  stars  more  or  less  remote. 

''  A  comparison  of  the  two  eixtremet  of  the  series,  as  a  coarse 
cluster  and  a  nebulous  star,  indicates,  however,  that  the  nebudonty 
about  the  darU  not  of  a  starry  nature. 

"  Considering  H,  iv.  69,  as  atypical  nebulous  star,  and  supposing 
the  nucleus  and  chevelure  to  be  connected,  we  may,  first,  suppose 
tlic  whole  to  be  of  stars,  in  which  case  either  the  nucleus  is  enor- 
mously larger  than  other  stars  of  its  stellar  magnitude,  or  the  envelo{Mi 
is  compoiied  of  stars  indefinitely  small ;  or,  second,  we  must  admit 
that  the  star  is  invched  in  a  lihmiag  fluid  of  a  natwrt  totatttfurUmown 

to  US.  \^ 

"  The  shining  fluid  might  exist  independently  of  stua.  The 
light  of  this  fluid  is  no  kind  of  reflection  from  the  star  in  the  cen- 
tre. If  this  matter  is  self-luminous,  it  seems  more  flt  to  produce  a 
star  by  its  condensation  than  to  depend  on  the  star  for  ita  exigence. 

"  Both  diffused  nebulosities  and  planetaiy  nebula  are  better 
nccounted  for  by  the  hypothesia  of  a  Bbining  fluid  than  by  mppos- 
ing  them  to  be  ^tant  atan.'* 

This  was  the  first  «cact  statement  of  the  idea  that,  beside 
stars  and  star-clusters,  we  have  in  the  nniverse  a  totally 
distinct  series  of  objects,  probably  mndi  more  simple  in 
their  constitution.  The  observations  of  Huooihs  and 
HvAXHi  on  the  spectra  of  these  bodies  have,  as  we  shall 
see,  entirely  confirmed  the  conclusions  of  Hebsohbl. 
'  Nebnlee  and  dusters  were  divided  by  Hkbsohsl  into 
classes.  Of  his  names,  only  a  few  are  now  in  general  use. 
He  applied  the  name  planetary  nebulcB  to  certain  oircnlar 
or  elliptic  nebula  which  in  his  telescope  presented  disks 
like  die  planets.  /^»ir<d  nebtila  are  tiiose  whose  convo- 
lutions have  a  spiral  shape.  This  class  is  quite  numer- 
ous. 

The  different  kinds  of  nebnlte  and  dusters  will  bo  better  under- 
stood from  the  cuts  and  descriptions  which  follow  than  by  formal 
definitions.  It  must  be  remembered  that  there  is  an  almost  infinite 
variety  of  such  shapes. 

The  figure  by  Sir  Johk  Hebschel  on  the  next  page  gives  a  good 
idea  of  a  spiral  or  ring  nebula.  It  has  a  central  nucleus  and  a  small 
and  bright  companion  nebula  near  it.  In  a  larger  telescope  than 
llBKscHEiN'a  its  aspect  is  even  more  complicated.  See  also  Fig.  138. 


5«S^f«iiBi»?«>'K»*»^w^a»":' 


iifjiHft.Hpwiii.  immjv  J 


AM 


ASTRONOMY. 


The  Omega  or  hor»c»h>e  nclnilu,  so  culled  from  the  resemblance 
of  the  briglitcct  end  of  it  to  a  Greek  Q,  or  to  a  horde's  iron  shoe,  is 
one  of  the  most  complex  and  remarkable  of  the  nebulae  visible  in 
the  northern  hemisphere.  It  is  particularly  worthy  of  note,  as 
there  is  some  reason  to  believe  that  it  has  a  proper  motion.  Cer- 
tain it  is  that  the  bright  star  which  in  the  figure  is  at  the  left-hand 
upper  comer  of  one  of  the  squares,  and  on  the  left-hand  (west) 
edge  of  the  streak  of  nebulosity,  was  in  the  older  drawtngs  placed 
on  the  other  side  of  this  streak,  or  within  the  dark  bay,  thus  mak- 
ing it  at  least  probable  that  either  the  star  or  the  nebula  has  moved. 


195;-~4PnUkIi  NKBOUL 


The  Uifid  nebula,  so  called  on  aocoont  of  its  three  branches 
which  meet  aeara  central  dark  space,  is  a  striking  object,  and 
was  suspected  by  Sir  Johh  Hebsohkl  to  have  a  proper  motion. 
Lator  observations  seem  to  confirm  this,  and  in  particular  th«  three 
bright  stars  on  the  left-hand  edge  of  the  right-hand  (east)  mass  are 
now  more  deeply  immersed  in  the  nebula  ftan  they  were  observed 
to  be  by  Hkbschkl  (1883)  and  Mason,  of  Yale  College  (1881),  In 
1784,  Sir  Wilmam  IlEBsciiEii  described  them  as  "  in  the  middle  of 
the  [dark]  triangle."  This  description  does  not  apply  to  their 
present  situation.    (Fig.  127). 


)in  the  rcsomblancu 
hoKu's  inm  shoo,  is 
le  nebulffi  visible  in 
worthy  of  note,  as 
Toner  motion.  Cer- 
re  18  at  the  left-hand 
the  left-hand  (west) 
lerdrawinm  placed 
lark  bay,  thus  mak- 
e  nebula  has  moved. 


its  three  branches 
itriking  object,  and 
ve  a  proper  motion, 
particular  th«  three 
lumd  (east)  mass  are 
they  were  observed 
College  (1887).  In 
18  "  in  the  middle  of 
I  not  apply  to  their 


4C2  ABTRONOMT. 


%  8.  STAB  0I.U8TMB8. 

The  most  note*!  of  all  the  duaten  k  the  PUtiade$,  which  have 
alieady  been  briefly  described  in  connection  with  the  constellation 
Totmu.  The  a^eraKe  naked  eje  can  easily  distingoish  t&x  stars 
wHhin  it,  bat  vnder  favorable  eoaditioM  ten,  eleven,  twelve,  or 


be  OMwted.    With  the  teleaeope,  over  ahaadred 

stars  arc  seen.  A  view  of  these  is  given  in  the  map  accompanying 
the  description  of  the  Pldadet,  Fig.  118,  p.  425.  This  group  con- 
tains Trmpbi/s  varia1)le  nebula,  so  callecl  liecause  it  has  been  sup- 
posed to  be  subject  to  variations  of  light.  This  is  probably  not  a 
variable  nebula. 


r-iwijw- 


I  ^f " 


NEnULAS  AND  OLUaTERS. 


463 


Pteiade$t  which  have 
irith  the  conatellation 
distlngidsh  rix  ttara 
tent  eleven,  twelve,  or 


The  chifltcra  rnnrcscntiHl  in  Figs.  120  and  IHO  arc  goml  cxampIvR 
of  their  cInsacH.  The  flrat  is  globular  and  containH  st^vnntl  thousand 
small  stars.  The  central  regions  are  densely  |)ackud  with  stars, 
and  from  these  radiate  curved  hairy-looking  branches  of  a  ipiral 
form.  The  second  is  a  cluster  of  about  200  stars,  of  nuigniludcs 
varying  from  the  ninth  to  the  thirteenth  and  fourteenth,  in  which 
the  hnghter  stars  are  scattered  in  a  somewhat  unusual  manner 


Bleaoope,  over  kluiBdred 

the  map  accompanying 

425.     This  group  con- 

because  it  has  been  sup- 

This  is  probably  not  a 


Flu.   128. — THB  BINO  RBBin^A  IN  LTBA. 

over  the  teleaco|dc  Held.  This  duster  is  an  excellent  example  of 
the  "  compressed  **  form  so  frequently  exhibited.  In  clusters  of 
this  class  the  spectroscope,  shows  that  each  of  the  individual  stars 
is  a  true  sun,  shining  by  its  native  brightness.  If  we  admit  that  a 
cluster  is  real — that  is,  that  we  have  to  do  with  a  collection  of  stars 
physically  connected — the  globular  dusters  become  important.  It 
IS  a  fact  of  observation  that  in  general  the  stars  composing  such 


K*-' 


n.\  .mimum. 


404 


A8TnoN0MY. 


vlustors  arc  aliout  of  c<|iial  niafrnitiiik-,  nnil  arc  more  eondciiHcd  at 
the  centre  than  at  tlic  edges.     They  are  prohably  8iil>je<t  to  central 

Jmwers  or  forces.  This  wua  seen  by  Bir  William  IIuiuc-iiul  in  178<.l. 
le  says  : 

"  Not  only  wore  routid  nobulic  and  clusters  formed  by  central 
powers,  but  likewise  every  cluster  of  8<tars  or  nebula  that  shows  a 
gradual  condensation  or  increasing  brightness  toward  a  centre. 
This  theory  of  central  power  is  fully  established  on  grounds  of  ob- 
servation which  cannot  \m  overturned. 

*' Cliuters  can  be  found  of  10  diameter  with  a  certain  desree  of 
''omprewion  and  stars  of  a  certain  magnitude,  and  smaller  clusters 
of  4 ,  S'  or  8'  in  diameter,  with  smaller  stars  and  greater  compression, 
and  so  on  through  resolvable  nebulsB  by  imperceptible  steps,  to  the 
smalleat  and  famtaat  land  most  distant]  nebula.    Other  clusters 


PlO.  IM.— •UMHILUl 


thete  an,  wMoh  lead  to  the  belief  that  dther  they  are  more  com- 
praased  or  are  composed  of  Iwrger  stars.  Spherical  dusters  are 
pimbably  not  more  different  in  ma  among  themsAlves  than  different 
individuals  of  planta  of  the  same  species.  As  it  has  been  shown 
that  the  sphericM  figure  of  a  cluster  of  stars  is  owing  to  central 
powers,  it  follows  tnt  those  clusters  which,  emUrit  panbtu,  are  the 
most  complete  in  this  figure  must  have  been  the  longest  exposed 
to  the  action  of  these  causes. 

"  The  maturity  of  d  sidereal  system  may  thus  be  judged  from 
the  dispositioii  of  :the  component  ports. 

"  Though  we  cannot  see  any  individual  nebula  pass  through  all 
its  stages  of  life,  we  can  select  particular  ones  m  each  peculiar 
stage,"  and  thus  obtain  a  single  view  of  their  entire  course  of  de- 
velopment. 


NKUULjB. 


4«;5 


B  more  condt'iiHcd  iit 
Illy  8ul)jcft  to  ci'iitriil 
M  IIEIWCIIKL  ill  1781). 

»  formed  by  central 

nebula  that  showB  a 

i>R8  toward  a  centre. 

id  on  grounds  of  ob- 

th  a  certain  desree  of 
and  smaller  cTusterH 
.  greater  compremlon, 
rceptible  steps,  to  the 
wke.    Other  cluatent 


Mr  they  are  more  com- 
^horicat  clastera  arc 
BmselTesthan  different 
Ab  it  has  been  shown 
ra  is  owing  to  central 
eaterU  panhu,  are  the 
1  the  longest  exposed 

thus  be  judged  from 

ibula  pass  through  all 
ones  m  each  peculiar 
oir  entire  course  of  de- 


g  4.    SFEOTBA  OF  NEBUUB  AKD  OLUSTEBS. 

Ill  1HU4,  tlvo  years  after  the  invention  of  tlic  s|M!ctrosco|K>,  Dr. 
HiuKiiNH,  uf  Jjondun,  commenced  the  examination  of  the  spectra 
of  tlic  ncbultc,  and  was  le<l  to  the  discovery  that  while  the  siiectru 
of  Htars  were  invariably  continuous  and  crossed  with  dark  lines 
similar  to  those  of  the  solar  siiectrum,  those  of  many  nebula)  were 
ilimmtinumi*,  showing  these  bodies  to  bo  composed  of  glowing  gos. 
The  tigure  shows  the  8])cctrum  of  one  of  the  most  famous  planetary 
ncbulic.  (II.  iv.  37.)  The  gaseous  nebulsB  include  nearly  all  tho 
planetary  nebulas,  and  very  frequently  liave  stellar-like  condensa- 
tions in  the  centre. 

Singular  enough,  the  most  milky  looking  of  any  of  the  nebula: 
(that  in  Andrometla)  gives  a  continuous  8|tc(;truni,  while  the  nebula 
uf  Orion,  which  fairly  glistens  with  small  stars,  has  a  discontinuous 


Via.   181.— flPECTBUH  or  a  FliAHKTART  VUBVhA. 

spectrum,  showing  it  to  be  a  true  ^.  Most  of  these  stars  are  too 
faint  to  be  separately  examined  with  the  8pectrosco|K>,  so  that  we 
cannot  say  whether  they  have  the  same  spectrum  as  the  nebulee. 

The  spectrum  of  most  clusters  is  continuous,  indicating  that  the 
individual  stars  are  truly  stellar  in  their  nature.  In  a  few  cases, 
however,  clusters  are  composed  of  a  mixture  of  nebulosity  (usually 
near  their  centre)  and  of  stars,  and  the  spectrum  in  such  cases  is 
compoun'T^  in  its  nature,  so  as  to  indicate  radiation  both  by  gaseous 
and  aoU  .  >  v^tter. 

§  6.   DISTBEBXmON  OF  NEBXTUB  Ain>  OLUSTEBS 
Onr  THE  SXTBFAOE  OF  THE  CELES- 
TIAL SFHEBE. 

The  follovring  map  (Pig.  182)  by  Mr.  R.  A.  Pboctob,  gives  at  a 
glance  the  distribution  of  the  nebulee  on  the  celestial  s])here  with 
reference  to  the  Milky  Way,  whose  boundaries  only  arc  indicated. 


UTAJt-Ol.USrKlUi 


407 


Tlio  iMiHitlon  of  ca<;li  iii!l)ulii  Ih  inarkud  l>y  n  clot ;  whuro  tlio  dotn  iiro 
thifki'Ht  tlioro  iH  u  region  rich  in  nolnilic.  A  cftHual  oxiimiuution 
shown  that  such  rich  regions  arc  UiHtant  from  the  Oahixy,  ami  it 
would  apiKjar  that  it  in  a  general  law  that  the  ncbulie  are  diHtri- 
Itutcd  in  greatcHt  numlHjr  around  the  two  \h>\c»  of  the  gala<tic 
circle,  ami  that  in  a  general  way  their  number  at  any  |X)int  of  the 
Holiero  IncroaMcs  with  their  di«tanco  from  thin  circle.  Thin  wuk 
noticed  by  the  elder  IIrhhchrI',  who  constructed  a  map  similar  to 
the  one  given.  It  is  precisely  the  rovcrHc  of  the  law  of  apparent 
distribution  of  the  true  star-clusters,  which  in  general  lie  in  or  near 
the  Milky  Way. 


m: 


x.m  iiii>,in'.  V  I''  "»<  U.-'.  -.IW>  ' 


CHAPTER    V. 


Sl'ECTIlA  OF   FIXED    STAUS. 


1.    0HABA0TBB8  OF   BTELLAB  BFEOTBA. 

Soon  after  thu  tllscovory  of  the  Hpcctro8co|»o,  Dr.  HuofUNB  and 
Profcsflor  W.  A.  Mii4.kh  applied  thfa  inHtriiinuiit  to  the  examina- 
tion of  BtoUar  spectra,  which  were  found  to  be,  in  tlie  main,  similar 
to  the  solar  spectrum— i.e.,  composed  of  a  continuous  band  of  the 

f)ri8mtttic  colors,  across  which  dark  lines  or  bands  were  laid,  the 
attor  iK'ing  Wxcd  in  position.  These  results  showed  the  fixed  stars 
to  resemble  our  own  sun  in  gentral  constitution,  and  to  be  com- 
posed of  an  incandescent  nucleus  surrounded  by  a  gaseous  and 
absorptive  atmosphere  of  lower  temiteraturo.  This  atmosphere 
around  many  stars  is  different  in  constitution  from  that  of  the  sun, 
as  is  shown  by  the  different  position  and  intensity  of  the  various 
black  lines  and  bands.  .«   ,  ,      «  s  * 

The  various  stellar  spectra  have  iMJcn  classined  by  Bkcchi  into 
four  t}n>e»,  distinguished  from  one  unother  by  marked  differences  in 
the  position,  character,  and  number  of  the  dark  lines. 

Type  I  is  comitosed  of  the  white  stars,  of  which  Hinu*  and  Vega 
are  examples  (the  upper  spectrum  in  the  plate  Fig.  1»8).  The  snec- 
tnim  of  these  stars  is  continuous,  and  is  crossed  by  four  dark 
lines,  due  to  the  presence  of  large  quantities  of  hydrogen  in 
the  envelope.  Sodium  and  magnesium  lines  are  also  seen,  and 
others  yet  niinter. 

Type  II  is  composed  mainly  of  the  yellow  stars,  like  our  own 
»m,^retunu,  Capella,  Aldtbaran,  and  Pdlux.  The  spectrum  of 
the  Bun  is  shown  in  the  second  place  in  the  plate.  The  vast  ma- 
jority of  the  stars  visible  to  the  naked  eye  belong  to  this  class. 

TVpe  III  (see  the  third  and  fourth  spectra  in  the  plate)  is  com- 
posed of  the  brighter  reddish  stars  like  a  OrUmis,  Antarea,  a  Hereulu, 
etc.  These  spectra  are  much  contracted  toward  the  violet  end,  and 
are  crossed  by  eight  or  more  dark  bands,  these  bands  being  them- 
selves resolvable  into  separate  lines.  ..  ,^  ,  . ,  .  j  u  « 
These  three  types  comprise  nearly  all  the  lucid  stars,  and  it  is 
not  a  little  remarkable  that  the  essential  differences  between  the 
three  classes  were  recognized  by  Sir  Wiiaiam  Herschkl  as  early 
as  1798,  and  published  in  1814.  Of  course  his  observations  were 
made  without  a  slit  to  his  spectroscopic  apparatus. 


us. 


BFEOTBA. 

Dr.  HuoctiNB  and 
t  to  the  cxamini^ 
thu  main,  Himilar 
nuous  bund  of  tho 
dB  weru  laid,  the 
vcd  tlie  flxod  stara 
and  to  be  com- 
ty  a  gaiteouB  and 
Thia  atmoflphore 
n  tliat  of  the  sun, 
lity  of  the  various 

A  by  Skcciii  into 
rkcd  differences  io 
iini'H. 

:li  Hirius  and  Vega 
g.  188).  Tlie  snec- 
«ed  by  four  dark 
I  of  hydrogen  in 
re  also  seen,  and 

irs,  like  our  own 
The  spectrum  of 
;e.  The  vast  mi^ 
r  to  this  class. 
:he  plate)  is  com- 
intaret,  a  Hermlit, 
he  violet  end,  and 
tHinds  being  them- 

cid  stars,  and  it  is 
inces  between  the 
iBRscHKii  as  early 
observations  were 

IS. 


UrKLLAH  srhxJV'ltA. 


401) 


•> 


aa 


OH 


mm^imty^f-  m .  ■.4<juJi.ii»W>'^';il«t'»!»*WWy I'!**!*'!  'WiWtJ'  fiflpM  ■ 


470 


ASTRONOMY. 


Typo  IV  comprises  the  red  stars,  which  are  mostly  telescopic. 
The  characteristic  spectrum  is  shown  in  the  last  figure  of  the  plate. 
It  is  curiously  banded  with  three  bright  spaces  ■epo'ated  by 
darker  ones. 

It  is  probable  that  the  hotter  a  star  is  the  more  simple  a  spectrum 
it  has  ;  for  the  brightest,  and  therefore  probably  the  hottest  stars, 
such  as  8iriu$,  give  spectra  ahowing  only  yery  thick  hydrogen  linea 
and  a  few  Terr  thin  metallic  lines,  while  the  cooler  stars,  such  as 
our  sun,  are  shown  by  their  spectra  to  contain  a  much  larger  num- 
ber of  metallic  elements  than  stars  of  the  type  of  Sirivs,  but  no 
non-metallic  elements  (oxygen  possibly  excepted).  The  coolest 
stars  give  band-flpectra  characteristic  of  compounds  of  metallic 
with  non-metallic  elements,  and  of  the  non-mctaUic  elements  un- 
combiued. 


^  a.    MOTZOH  OF  STABS  JS  THE  ZJNE  OF  SIQHT. 


Spectroscopic  observations  of  stars  not  only  give  information  io 
regard  to  their  chemical  and  physical  constitution,  but  have  been 
applied  so  ns  to  determine  approximately  the  velocity  in  kilometres 
per  second  with  which  the  stars  are  approaching  to  or  receding 
from  the  earth  along  the  line  joining  earth  and  star.  The  theory 
of  such  a  determination  is  briefly  as  follows : 

In  the  solar  spectrum  we  find  a  ^up  of  dark  lines,  as  a,  },  «, 
which  always  maintain  their  relative  position.  From  laboratory 
experiments,  we  can  show  that  the  three  bright  lines  of  incandescent 
hydrogen  (for  example)  have  always  the  same  relative  position  as 
the  solar  dark  lines  a,  1,6.  From  this  it  is  inferred  that  the  solar 
dark  lines  are  due  to  the  presence  of  hydrogen  in  it*  absorptive 
atmosphere. 

Now,  suppose  that  in  a  stellar  spectrum  we  find  three  dark 
lines  a',  V,  e',  whose  relative  position  is  exactly  the  same  as  that 
of  the  solar  lines  a,  b,  e.  Not  only  is  their  relative  position  the 
same,  but  the  characters  of  the  lines  themselves,  so  far  as  the  fainter 
spectrum  of  the  star  will  allow  us  to  determine  them,  are  dso  nmi- 
lar— that  is,  a'  and  a,  V  and  I,  e'  and  e  are  alike  as  to  thickness, 
blackness,  nebulosity  of  edges,  ete.,  ete.  From  this  it  is  infened 
that  the  star  really  contains  m  its  atmosphere  the  substance  whose 
existence  has  been  shown  in  the  sun. 

If  we  contrive  an  apparatus  by  which  the  stellar  spectrum  is  seen 
in  the  lower  half  (say)  of  the  eye-piere  oi  the  spectroscope,  while 
the  spectrum  of  hydrogen  is  seen  just  above  it,  we  find  in  some 
cases  this  remarkable  phenomenon.  The  three  dark  stellar  lines, 
a',  &',«',  instead  of  being  exactly  coincident  with  the  tiiree  hydro- 
gen Unes  a,h,e,  are  seen  to  be  all  thrown  to  one  side  or  the 
other  by  a  like  amount— that  is,  the  whole  group  a',  J',  e,  while 
preserving  its  relative  distances  the  same  as  those  of  the  omnpivi- 
son  group  a,  ft,  e,  is  shifted  toward  either  the  violet  or  red  end  of 
the  spectrum  by  a  small  yet  measurable  amount.    Bepei^  expert- 


mostly  telescopic. 
;  figure  of  the  plate, 
jaces  ■epa'ated  by 

e  simple  a  spectrum 
ly  the  hottest  stars, 
liick  hydrogen  lines 
ooler  stars,  such  as 
I  much  larger  num- 
3  of  Siriut,  but  no 
ted).  The  coolest 
pounds  of  metallic 
itallio  elements  un- 


KE  or  siaHT. 

give  information  ic 
ion,  but  have  been 
ilocity  in  kilometres 
ling  to  or  receding 
d  star.    The  theory 

irk  lines,  wa,  h,t, 
From  laboratory 
ines  of  incandescent 
relative  position  as 
erred  that  the  solar 
n  in  its  absorptive 

ve  find  three  dark 
tly  the  same  as  that 
alative  position  the 
,  so  f ar  M  the  fainter 
them,  are  also  nmi- 
ke  as  to  thickness, 
n  this  it  is  infened 
le  substance  whose 

lar  speotrum  is  seen 
spectroscope,  while 
i,  we  find  in  some 
>  dark  stellar  lines, 
ith  the  three  hydro- 
to  one  side  or  the 
oup  a',  h'j  tf,  while 
>8e  of  the  omnpari- 
riolet  or  red  end  of 
Repeated  expeii- 


■aBwy.<rf  Mi"J''»uiiW!'i<iiH'>u«Mtwmi.«i^«nw»<ii 


STELLAR  SPJSGTltA. 


471 


mentB  by  diffurent  instruments  and  observers  show  always  a  shifting 
in  the  same  direction  and  of  like  amount.  The  figure  shows  the 
shifting  of  the  F  line  in  the  spectrum  of  Sirvut,  compared  with  one 
fixed  line  of  hydrogen. 

This  displacement  of  the 
spectral  Imes  is  now  ac- 
counted for  by  a  motion  of 
the  star  toward  or  from  the 
earth.  It  is  shown  in  Phy- 
sics that  if  the  source  of 
the  light  which  gives  the 
spectrum  a',  V,  e  is  mov- 
ing away  from  the  earth,thi8 
group  will  be  shifted  toward 
the  red  end  of  the  spec- 
trum ;  if  toward  the  earth, 
then  the  whole  group  will 
be  shifted  toward  the  blue 
end.  The  amount  of  this 
shifting  is  a  function  of  the 
velocity  of  recession  or  ap- 
proach, and  this  velocity  m 
miles  per  second  can  be 
calculated  from  the  meas- 
ured displacement.  This  has  been  done  for  many  stars  by  Dr. 
HvoaiNS,  Dr.  Vookl,  and  Mr.  C'ubibtib.  Their  results  agree  well, 
when  the  difllcult  nature  of  the  research  is  considered.  The  rates 
of  motion  vary  from  insensible  amounts  to  100  kilometres  per  sec- 
ond ;  and  in  some  cases  agree  remarkably  with  the  velocities  com- 
puted from  the  proper  motions  and  probable  parallaxes. 


Fio.  131— p-um  iH  entcTRcif  of 
snuvs. 


CHAPTER  VI. 


MOTIOJJS  AND  DISTANCES  OF  THE  STAllS. 


§  1.    FBOFSB  MOTIONS. 

Wk  havo  already  stated  that,  to  the  unaided  vision,  tlio 
fixed  stars  appear  to  preserve  the  same  relative  position  in 
the  heavens  through  many  centuries,  so  that  if  the  an- 
cient astronomers  once  more  saw  them,  they  could  hardly 
detect  the  slightest  change  in  their  arrangement.  But 
the  refined  methods  of  modem  astronomy,  in  which  the 
power  of  the  telescope  is  applied  to  celestial  measurement, 
have  shown  that  there  are  slow  changes  in  the  positions 
of  the  brighter  stars,  consisting  in  a  motion  forward  in  a 
straight  line  and  with  uniform  velocity.  These  motions 
aro,  for  the  most  part,  so  slow  that  it  would  require  thou- 
sands of  years  for  the  change  of  position  to  be  percepti- 
ble to  the  unaided  eye.     They  are  called  proper  moHons. 

As  a  general  rule,  the  fainter  the  atars  the  smaller  the  pro^r  mo- 
tions. For  the  most  part,  the  proper  motions  of  the  telescopic  stus 
are  so  minute  that  they  have  not  been  drteCMsd  except  in  a  very 
few  cases.  This  arises  partly  from  the  actual  slowness  of  the  mo- 
tion, and  partly  from  the  fadt  that  the  positions  of  these  stars  have 
not  generally  been  well  determined.  It  will  be  readily  seen  that,  in 
order  to  detect  the  proper  motion  of  a  star,  its  position  must  be  de- 
termined at  periods  separated  by  considerable  intervals  of  time. 
Since  the  exact  determinaUons  of  star  positions  Jia'  only  been 
made  since  the  year  1750,  it  follows  that  no  proper  motion  can  be 
detected  unless  it  is  hu^  enough  to  become  perceptible  at  the  end 
of  a  centurr  and  a  quarter,  mth  very  few  ezcepnons,  no  accurate 
determination  of  the  positions  of  telescopic  stars  was  made  until 
about  the  beginning  of  the  present  century.  Consequently,  we 
cannot  yet  pronounce  upon  the  proper  motions  of  these  stara,  and 


THE  STAllS. 

naidcd  vision,  tho 
'elative  position  in 
K)  that  if  the  an- 
they  could  hardly 
Tangemcnt.  But 
liny,  in  which  the 
itiai  measurement, 
!8  in  the  positions 
ition  forward  in  a 
.  These  motions 
>uld  require  thou- 
in  to  be  percepti- 
1  proper  moUona. 

nailer  the  proper  mo- 
>f  the  telescopic  stus 
:>M9d  except  in  a  verj 

slowneM  of  the  mo- 
18  of  these  stars  have 
I  readily  seen  that,  in 

position  must  be  de- 
le intervals  of  time, 
ions  ha.'  onlj  been 
»roper  motion  can  be 
erceptible  at  the  end 
cepnons,  no  acemate 
stars  waa  made  until 
Consequently,  we 
B  of  these  stan,  and 


MOTIONS  OF  TJIK  STARS. 


473 


can  only  say  that,  in  general,  they  arc  too  small  to  bo  detected  by 
the  observations  hitherto  made. 

To  this  rule,  that  the  smallor  stars  have  no  sensible  proper  mo- 
tions, there  are  a  few  very  notable  exceptions.  The  star  Oroom- 
hrUIge  1830,  is  remarkable  for  having  the  greatest  proper  motion  of 
any  in  the  heavens,  amounting  to  about  7'  in  a  year.  It  is  only  of 
tlic  seventh,  magnitude.  Next  in  the  order  of  pro))cr  motion  comes 
tlic  double  star  61  Gygni,  which  is  alraut  of  the  fifth  magnitude. 
There  are  in  all  seven  small  stars,  all  of  which  have  a  larger  proper 
motion  than  any  of  the  first  magnitude.  But  leaving  out  these  ex- 
ceptional cases,  the  remaining  stars  show,  on  an  average,  a  diminu- 
tion of  proper  motion  with  brightness.  In  ceneral,  the  proper 
motions  even  of  the  brightest  stars  are  only  a  fraction  of  a  second 
in  a  year,  so  that  thousands  of  years  would  be  required  for  them 
to  change  their  place  in  any  striking  degree,  and  hundreds  of 
thousands  to  make  a  complete  revolution  around  the  heavens. 


%  2.   PBOFEB  HOnON  OF  THE  SUN. 

A  very  interesting  result  of  the  proper  motions  of  tlic 
stars  is  that  our  sun,  considered  as  a  star,  has  a  consider- 
able proper  motion  of  its  own.  By  olwervations  on  a  star, 
we  really  detennine,  not  tho  proper  motion  of  the  star  it- 
self, but  the  relative  proper  motion  of  the  observer  and 
the  star — that  is,  the  difference  of  their  motions.  Since 
the  earth  with  the  observer  on  it  is  carried  along  with  the 
sun  in  space,  his  proper  motion  is  the  same  as  that  of  the 
sun,  so  that  what  observation  gives  us  is  the  difference 
l)etween  the  proper  motion  of  the  star  and  that  of  the  sun. 
There  is  no  way  to  determine  absolutely  how  much  of 
the  apparent  proper  motion  is  due  to  the  real  motion  of 
the  star  and  how  nmch  to  the  real  motion  of  the  sun.  If, 
however,  we  find  that,  on  the  average,  there  is  a  lai'ge  pre- 
ponderance of  proper  motions  in  one  direction,  we  may 
conclude  that  there  is  a  real  motion  of  the  sun  in  an  op- 
posite direction.  The  reason  of  this  is  that  it  is  more 
likely  that  the  average  of  a  great  mass  of  stars  is  at  rest 
than  that  the  sun,  which  is  only  a  single  one,  should  be  at 
rest.  I^ow,  obflervation  shows  that  this  is  really  the  case, 
and  that  the  great  mass  of  stars  appear  to  be  moving  from 
the  direction  of    the  xM>nstel1ation  Hercules  and  toward 


mmsmimmsmmmm 


474 


ASTRONOMT. 


that  of  the  constellation  Argots.*  A  number  of  astrono- 
more  have  investigated  this  motion  with  a  view  of  deter- 
mining the  exact  point  in  the  heavens  toward  which  tlie 
gun  is  moving.  Their  results  are  shown  in  the  following 
table : 


ArfreUnder 

O.  Strove 

Land»bl 

Oalloway 

MAdler 

Airy  and  Dunkin 


DaoltwUlon. 


It  will  be  perceived  that  there  is  some  discordance  aris- 
ing from  the  diverse  characters  of  the  motions  to  be  in- 
vestigated. Yet,  if  we  lay  these  different  points  down  on 
a  map  of  the  stars,  we  shall  find  that  they  all  fall  in  the 
constellation  HerGvUa.  Tlie  amount  of  the  motion  is  such 
that  if  the  sun  were  viewed  at  right  angles  to  the  direction 
of  motion  from  an  average  star  of  the  first  magnitude,  it 
would  appear  to  move  about  one  tlurd  of  a  second  per 
year. 

g  3.   DISTAITGES  OF  THE  FEEBD  STABS. 

The  problem  of  the  distance  of  the  stars  has  always 
been  one  of  the  greatest  interest  on  account  of  its  involv- 
ing the  question  of  the  extent  of  the  visible  universe. 
The  ancient  astronomers  supposed  all  the  fixed  stars  to  be 
situated  at  a  short  distance  outside  of  the  orbit  of  the  planet 
Saturn,  then  the  outermost  known  planet.  The  idea  was 
prevalent  that  Nature  would  not  waste  space  by  leaving  a 
great  region  beyond  Saturn  entirely  empty.. 

When  CopEKNious  announced  the  theory  that  the  eon 
was  at  rest  and  the  earth  in  motion  around  it,  the  prob- 
lem of  the  distance  of  the  stars  acquired  a  now  interest 
*  This  was  diBcovoKd  by  Sir  Wiuuam  Hbhbobbl  in  118S. 


DISTANCES  OF  THE  STARS. 


4'^5 


imber  of  astrono- 
I  a  view  of  deter- 
toward  which  tlic 
I  in  the  following 


DaeliwUion. 

88°    SC    N 
87 


36'  N. 

26'  N. 

23'  N. 

8»°    54'  N. 

28°    68'  N. 


14° 
84° 


)  discordance  aris- 
motions  to  be  in- 
int  points  dovm  on 
[ley  all  fall  in  the 
the  motion  is  such 
les  to  the  direction 
lirst  magnitude,  it 
,  of  a  second  per 

3D  STABS. 

I  stars  has  always 
ouut  of  its  involv- 
)  visible  univorac. 
le  fixed  stars  to  bo 
( orbit  of  the  planet 
let.  The  idea  was 
space  by  leaving  a 
ipty. 

eory  that  the  snn 
»nnd  it,  the  prob- 
ad  a  now  interest 

tBBCBBL  in  1788. 


It  was  evident  that  if  the  earth  described  an  annual  orbit, 
then  the  stars  would  appear  in  the  course  of  u  year  to  os- 
cillate back  and  forth  in  corresponding  orbits,  unless  they 
were  so  immensely  distant  that  these  oscillations  were  too 
small  to  be  seen.  Now,  the  apparent  oscillation  of  Saturn 
produced  in  this  way  was  described  in  Fart  I. ,  and  sliown 
to  amount  to  some  6°  on  each  side  of  the  mean  position. 
These  oscillations  were,  in  fact,  those  which  the  ancients 
represented  by  the  motion  of  the  planet  around  a  small 
epicycle.  But  no  such  oscillation  had  ever  been  detected 
in  a  fixed  star.  This  fact  seemed  to  present  an  almost 
insuperable  difficulty  in  the  reception  of  the  Copemican 
system.  This  was  probably  the  reason  why  Tvoho  Bbahk 
was  led  to  reject  the  system.  Very  naturally,  therefore, 
as  the  instruments  of  observation  were  from  time  to  time 
improved,  this  apparent  annual  oscillation  of  the  stars  was 
ardently  sought  for.  When,  about  the  year  1704, 
BoEMEB  thought  he  had  detected  it,  he  published  his  ob- 
servations in  a  dissertation  entitled  '*  Copernicus  Trium- 
jphansy  A  similar  attempt,  made  by  IIrM)KB  of  England, 
was  entitled  *^  An  Attempt  to  Prove  the  Motion  of  the 
Eiirth:' 

This  problem  is  identical  with  that  of  the  annual  paral- 
lax of  the  fixed  stars,  which  has  been  already  described  in 
the  concluding  section  of  our  opening  chapter.  This 
parallax  of  a  heavenly  body  is  the  angle  which  the  mean 
distance  of  the  earth  from  the  snn  snbtends  when  seen 
from  the  body.  The  distance  of  tlie  body  from  the  snn  is 
inversely  as  the  parallax  (nearly>.  Thus  the  mean  distance 
of  Saturn  being  9*5,  its  annual  parallax  exceeds  6°,  while 
that  of  NepbrniSy  which  is  three  times  as  far,  is  abont  2°. 
It  was  very  evident,  without  telescopic  observation,  that 
the  stars  could  not  have  a  parallax  of  one  half  a  degree. 
They  must  therefore  be  at  least  twelve  times  as  far  as 
Saturn  if  the  Oo]iemican  system  were  true. 

When  the  telescope  was  applied  to  measurement,  a  eon- 
tinually  increasing  accuracy  began  to  he  gained  by  the 


mam 


f/mi¥m 


476 


AUTllONOMY. 


i  ii 


improvement  of  the  instruments.  Yet  for  Bevoral  genera- 
tions the  purallux  of  the  fixed  stars  eluded  nieasurenient. 
Very  often  indeed  did  observers  think  they  had  detected 
a  parallax  in  some  of  the  brighter  stars,  but  their  succes- 
sors, on  repeating  their  measures  with  better  instruments, 
and  investigating  their  motltods  anew,  found  their  con- 
clusions erroneous.  Early  in  the  present  century  it  l)e- 
came  certain  that  even  the  brighter  stars  had  not,  in  gen- 
oral,  a  parallax  as  groat  as  1",  and  thus  it  became  certain 
that  they  must  lie  at  a  greater  distance  than  2CH),00<)  times 
that  which  separates  the  earth  from  the  sun. 

Success  in  twtually  measuring  the  parallax  of  the  stars 
was  at  length  obtained  almost  simultaneously  by  two  as- 
tronomers, l^KssKt.  of  Kiinigslierg,  and  Stbuvk  of  Dorpat. 
Bkssbl  selected  for  his  star  to  lie  observed  01  Cytjni,  and 
commenced  his  observations  on  it  in  August,  1837.  The 
result  of  two  or  three  years  of  oliservation  was  that  this 
star  had  a  panUlax  of  0*  •  35,  or  about  one  third  (»f  a  sec- 
ond. This  would  make  its  distance  from  the  sun  nearly 
fiO(),00()  astronomical  units.  The  reality  of  this  paral- 
lax has  I)oen  well  established  by  subsequent  investigators, 
only  it  has  been  shown  to  be  a  little  larger,  and  therefore 
the  star  a  little  nearer  than  Bksskl  supposed.  The  most 
probable  parallax  is  now  found  to  be  0'  •  51,  corresponding 
to  a  distance  of  400,000  radii  of  the  earth's  orbit. 

The  star  selected  by  Strcvr  for  the  meaaure  of  parallax  was  the 
bright  one,  a  Lurm.  His  observations  were  made  between  Novem- 
ber, 18S5,  and  August,  1888.  He  first  deduced  a  parallax  of  0'-25. 
Subsequent  observers  have  reduced  this  parallax  to  0'-20,  corre- 
sponding to  a  distance  of  about  1,000,000  astronomical  units. 

Short^  after  this,  it  was  found  by  HBHDBRaoN,  of  England,  As- 
tronomer Royal  for  the  Cape  of  Qood  Hope,  that  the  star  a  Cetdauri 
had  a  still  larger  parallax  of  about  1*.  This  is  the  largest  ptmllax 
now  known  in  the  case  of  any  fixed  star,  so  that  a  Cmtauri  is,  be- 
yond aP  reasonable  doubt,  the  nearest  fixed  star.  °  Tet  its  distance 
is  more  than  9lCiO,000  astronomical  imits,  or  thirty  millions  of  nat- 
ions of  kilometres.  Light,  which  passes  from  the  sun  to  the  earth 
in  8  minutes,  would  require  S^  years  to  reach  us  from  a  OttUauri, 

Two  methods  of  determining  parallax  have  been  applied  in  as- 
tronomy. The  paratUx  found  by  one  of  these  methods  is  known  as 
tAioliUe,  that  by  the  other  as  reutiee  paralku.    In  determining  the 


JJiaTANCES  OF  TUK  STAItH. 


477 


For  Bevoral  gonora- 
Itid  iiiuauureinuut. 
tliey  had  detected 
,  but  their  succes- 
>etter  instniinonts, 
,  found  their  con- 
ent  century  it  lie- 
's had  not,  in  gen- 
it  became  certain 
than  200,000  times 
sun. 

irallax  of  tlio  stars 
noously  by  two  as- 
Stbuvk  of  Dorpat. 
iTcd  01  Cyyni,  and 
ngust,  1837.  The 
ition  was  that  tliis 
one  tliird  <»f  a  sec- 
OHi  tlie  sun  nearly 
dity  of  this  paral- 
[uent  investigators, 
rger,  and  therefore 
>po8ed.  The  most 
•  51,  corresponding 
•th's  orbit. 

are  of  parallax  was  th« 
nade  between  Novem- 
sed  a  parallax  of  0'-25. 
mllaxto  O'-aO,  corre- 
tronomical  units. 
EiuoN,  of  England,  As- 
that  the  star  a  Oentauri 
is  the  largest  parallax 
that  a  Centauri  is,  be- 
star.  '  Yet  its  distance 
thirty  millions  of  mlli- 
>m  tiie  sun  to  the  earth 
1  OS  from  a  Outtawri. 
ra  been  applied  in  as- 
le  methods  is  known  as 
t.    In  determining  the 


ikksoliitu  piirallax,  the  observer  finds  thu  \wlvLr  distanco  nf  the  tttar 
im  often  as  possible  through  a  period  of  one  or  more  years  with  a 
moriilian  circle,  and  then,  by  a  discussion  of  all  his  observations, 
conchulus  what  is  the  magnitude  of  thu  oscillation  duo  to  parallax. 
The  difficulty  in  applying  this  method  is  that  the  refraction  of  the 
air  and  the  state  of  the  instrument  are  subject  to  changes  arising 
from  varying  temperature,  so  that  the  observations  are  always  un- 
certain by  an  amount  which  is  important  in  such  delicate  work. 

In  determining  the  relative  paraUax,  the  astronomer  selects  two 
stars  in  the  same  field  of  view  of  his  tele8C0]M:,  one  of  which  is 
many  times  more  distant  than  the  other.  It  is  possible  to  judge 
with  a  high  degree  of  probability  which  star  is  the  more  distant, 
from  the  magnitudes  and  proper  motions  of  the  two  objects.  It  is 
nsMumed  that  a  star  which  is  either  very  bright  or  has  a  largo  pro- 
])cr  motion  is  many  times  nearer  to  us  than  the  extremely  faint 
stars  which  may  be  nearly  always  seen  around  it.  The  effect  of 
parallax  will  then  be  to  change  the  apparent  position  of  the  bright 
star  among  the  small  stars  around  it  in  the  course  of  a  year.  This 
(iliango  admits  of  being  measured  with  great  precision  by  the  mi- 
crometer of  the  equatorial,  and  thus  the  relative  parallax  may  be 
determined. 

It  is  true  that  this  relative  parallax  is  really  not  the  absolute  par- 
allax of  either  body,  but  the  difference  of  their  parallaxes.  So  we 
must  necessarily  suppose  that  the  parallax  of  the  smaller  and  more 
distant  object  Is  zero.  It  is  bythis  method  of  relative  parallax 
that  the  great  majority  of  determinations  have  been  made. 

The  distances  of  the  stars  are  sometimes  expressed  by 
the  time  required  for  light  to  pass  from  tliem  to  our  sys- 
tem. The  velocity  of  hght  is,  it  will  be  remembered, 
about  300,000  kilometres  per  second,  or  such  as  to  pass 
from  the  sun  to  the  earth  in  8  minutes  18  seconds. 

The  time  required  for  light  to  reach  the  earth  from 
some  of  the  stats,  of  which  the  parallax  has  been  measured, 
is  as  follows : 


StAK. 

Tmr. 

Stab. 

Yean. 

a  Oeniatiri 

8-5 
6-7 
83 

eo 

••4 
10-6 
11-9 
181 
18  7 
17-9 

70  OpkiwM. 

t  VnaMttjoTU.... 

Areturui 

Y  Draeonii 

1880  Qroombridge. 

Polorii 

19- 1 

61  qnni 

21,115  Lalandtt 

«  Cmkmri 

itGaitieptia 

34  OroambrMov. . . . 
21,258  Lalan^k.... 

17,415  Oeltmi. 

afrJM 

94-8 
25-4 
851 
859 
^•4 

8077  Bradley. 

85  Ptgad 

461 
64>5 

aAwigei. 

0  DraeoniB^ 

70- 1 

u  Lgm 

1291 

i»w?itwL»WJ,ia!#ft^e^;a»sE?gsg^.fe'^^iy...'^%'..ai^ 


CHAPTER  VII. 

CONSTRUCTION  OF  TUB  HEAVENS. 

Thb  visible  univeree,  as  revealed  to  us  by  the  telescope, 
is  a  coUcction  of  many  mimons  of  stars  and  of  several 
thousand  nebuljB.  It  is  sometimefl  caUed  the  stellar  or 
sidereal  system,  and  sometimes,  as  already  remarked,  the 
stellar  universe.  The  most  far-reaching  question  with 
which  astronomy  has  to  deal  is  that  of  tlie  form  and  mag- 
nitude  of  this  system,  and  the  arrangement  of  the  stars 
which  compose  it. 

It  was  once  supposed  that  the  stars  were  arranged  on 
the  same  general  plan  as  the  bodies  of  the  solar  system, 
being  divided  up  into  great  numbers  of  groups  or  clus- 
ters, while  all  the  stars  of  each  group  revolved  in  regukr 
orbits  round  the  centre  of  the  group.  All  the  groups  were 
suppoBed  to  revolve  around  some  great  common  centre, 
which  was  therefore  the  centre  of  the  visible  universe. 

But  there  is  no  proof  that  this  view  is  correct.  The 
only  astronomer  of  the  present  century  who  held  any  such 
doctrine  was  Maedlkb.  He  thought  that  the  centre  of 
motion  of  all  the  stars  was  m  the  Pleiades,  but  no  other 
astronomer  shared  his  views.  "We  have  abeady  seen  that 
a  great  many  stars  are  collected  into  clusters,  but  there  is 
no  evidence  that  the  stars  of  these  dusters  revolve  in 
regukr  orbits,  or  that  the  dusters  themselves  have  any 
regular  motion  around  a  common  centre.  Besides,  the 
large  majority  of  stais  visible  with  the  telescope  do  not 
appear  to  be  grouped  into  dusters  at  alL 


8rnucTUiit!  OF  Tim  uka  vknh. 


479 


HEAVENS. 

IB  by  the  telescope, 
ars  and  of  several 
died  the  stellar  or 
3ady  remarked,  the 
ling  question  with 
tlie  form  and  mag- 
ement  of  the  stars 

B  were  arranged  ou 
)f  the  solar  system, 

of  groups  or  clus- . 
revolved  in  regular 
A.11  the  groups  were 
9at  common  centre, 
visible  universe. 
w  is  correct.    The 

who  held  any  such 
that  the  centre  of 
iades,  but  no  other 
ve  already  seen  that 
jlusters,  but  there  is 

dusters  revolve  in 
lemselves  have  any 
mtre.  Besides,  the 
le  telescope  do  not 
IL 


The  first  astronomer  to  make  a  careful  study  of  the 
arrangement  of  the  stars  with  a  view  to  learn  the  structure 
of  the  heavens  was  Sir  William  IIebschel.  lie  published 
in  the  PhiUm/phical  Transactions  several  memoirs  on  the 
construction  of  the  heavens  and  the  arnuigcmunt  of  the 
stars,  which  have  become  justly  celebrated.  We  s  liall 
therefore  begin  with  an  account  of  IIeksoiikl's  methods 
and  nsBults. 

IIeksoiiel'b  method  of  study  was  founded  on  a  mode  of 
observation  which  he  called  sta/r-gaiiging.  It  consisted  in 
pointing  a  powerful  telescope  toward  various  parts  of  the 
heavens  and  ascertaining  by  actual  count  how  thick  the 
Bturs  were  in  each  region.  His  20-foot  reflector  was  pro- 
vided with  such  an  eye-piece  that,  in  looking  into  it,  he 
would  see  a  portion  of  the  heavens  about  15'  in  diameter. 
A  circle  of  this  size  on  the  celestial  sphere  has  al)out  one 
quarter  the  apparent  surface  of  the  sun,  or  of  the  full 
moon.  On  pointing  the  telescope  in  any  direction,  a 
greater  or  less  number  of  stars  were  nearly  always  visible. 
These  were  counted,  and  tlie  direction  in  which  the  tele- 
scope pointed  was  noted.  Gauges  of  this  kind  were  made 
in  all  parts  of  the  sky  at  which  he  could  point  his  instru- 
ment, and  the  results  were  tabulated  in  the  order  of  right 
iiscension. 

Tlie  following  is  an  extract  from  the  gauges,  and  gives 
the  average  number  of  stars  in  each  field  at  the  points 
noted  in  right  ascension  and  north  polar  distance  : 


R.  P.  D. 

N.  P.  D. 

B.A. 

tr  toM° 

B.A. 

7B«  to80> 

Jlo  of  Stm. 

NaofStuiu 

h.         m. 

h.          m. 

15         10 

94 

11          6 

81 

16       88 

10-6 

IS       81 

8-4 

15       47 

106 

18       44 

46 

16         8 

181 

18       49 

8-9 

16       86 

18-6 

18         8 

8-8 

16       87 

18-6 

14       80 

86 

IW'WliiMliMWMIIWWi 


480 


ASmoNOMY. 


In  this  «iniill  tiiblo,  it  iw  plain  that  a  «liffuront  law  of 
cluHtcring  or  of  distrilmtion  obtaiiiH  in  the  two  rogiouH. 
Buch  diffurenees  aro  still  mor«  marked  if  wu  conipai-o  the 
oxtrenio  wuhjs  fonnd  by  IIkbsciikl,  aa  II.  A.  =  lU""  41"', 
N  P  D,  =  74°  33',  nuinbor  of  stars  \hst  field  ;  588, 
and  il.  A.  =  16"  10",  N.  P.  D.,  113°  4',  number  of 

stars  =  l-l. 

The  number  of  these  stars  in  certain  portions  is  very 
great.  For  example,  in  the  Milky  Way,  near  OrUm,  six 
fields  of  view  promiscuously  taken  gave  110,  60,  70,  90, 
70,  and  74  stars  each,  or  a  mean  of  79  stars  per  field. 
The  most  vacant  space  in  this  noighlwrhood  gave  63  stars. 
So  that  as  Herschkl's  sweepa  were  two  degrees  wide  in 
declination,  in  one  hour  (15°)  there  would  pass  through 
the  field  of  his  telescope  40,000  or  more  stars.  In  some 
of  the  sweeps  this  number  waa  as  great  as  116,000  stars 
in  a  quarter  of  an  hour. 

On  applying  this  telescope  to  the  Milky  Way,  IIeb- 
SOHBL  supposed  at  the  time  that  it  completely  resolved  the 
whole  whitish  appearance  into  small  stars.  Tliis  conclu- 
sion he  subsequently  modified.     He  says  : 

"  It  U  very  probable  that  the  great  stratum  called  the  Milky  Way 
is  that  in  which  the  sun  is  placed,  though  perhaps  not  in  the  very 
centre  of  its  thickness.  .  .^     „  ,  vi  u 

"We  gather  this  from  the  appearance  of  the  Galaxy,  which 
seems  to  encompass  the  whole  heavens,  as  it  certainly  must  do  if 
the  sun  is  within  it.  For,  suppose  a  number  of  stars  arranged  be- 
tween two  parallel  pbmes,  indefinitely  extended  every  way,  but  at 
a  given  considerable  distance  from  each  other,  and  calling  thU  a 
sidereal  stratum,  an  eye  placed  somewhere  within  it  will  see  all 
the  stars  in  the  direction  of  the  planes  of  the  stratum  projected  into 
a  great  circle,  which  will  appe&r  lucid  on  account  of  the  accumu- 
lation of  the  stars,  while  the  rest  of  tiiC  heavens,  at  the  sides,  will 
only  seem  to  be  scattered  over  with  constellations,  more  or  less 
crowded,  according  to  the  distance  of  the  planes,  or  number  of 
Stan)  contained  in  vm  thickness  or  sides  of  the  stratum." 

Thus  in  Hbrsobbl^b  figure  an  eye  at  8  within  the  stratum  ah 
will  see  the  stars  in  the  direction  of  its  length  al,  or  height  ed, 
with  all  those  in  the  intermediate  situations,  projected  into  the 
lucid  circle  A  OBD,  while  those  in  the  rides  me,  n»,  will  be  seen 
scattered  over  the  remaining  part  of  the  heavens  M  VlfW. 


STRUVTURE  OP  THE  HEA  VEN8. 


481 


a  «liffuront  law  of 
in  the  two  rogioiw. 

if  w«  coiiipiiTO  thu 
8  R.  A.  =  ID"  41'", 
ir»  jKsr  field;  588, 
113°  4',  number  of 

lin  portions  is  very 
ITay,  near  OrUm,  hIx 
ivo  110,  00,  70,  90, 
70  stars  per  field. 
)rhood  gave  63  stars, 
two  degrees  wide  in 
would  pass  through 
[ore  stars.  In  some 
■eat  as  116,000  stars 

3  Milky  Way,  IIeb- 
npletely  resolved  the 
stars.  Tliis  conclu- 
lays : 

im  called  the  Milky  Wsy 
perhaps  not  in  the  very 

I  of  the  Oalaxy,  which 
>  it  cerUdnly  must  do  if 
ter  of  stars  arranged  bc- 
ended  every  way,  but  st 
other,  and  calling  this  a 
re  within  it  will  see  all 
le  stratum  projected  into 
account  of  the  accumu- 
eavens,  at  the  rides,  will 
istellations,  more  or  less 
le  planes,  or  number  of 
<  the  stratum." 
Sr  within  the  stratum  ah 
length  al,  or  height  ed, 
ions,  projected  into  the 
des  tnv,nw,  will  be  seen 


"  If  the  eye  were  placed  somewhere  without  the  stratum,  at  no 
very  ^reat  (listance,  tho  apnearance  of  the  stars  within  it  would 
assume  the  form  of  one  of  tne  smaller  circles  of  the  sphere,  which 


Fio.  1S5.->-hbbbchbl'b  thbdbt  or  ths  stbixar  sveTBic. 

would  be  more  or  less  contracted  according  to  tho  distance  of  the 
eye ;  and  if  this  distance  were  exceedingly  increased,  the  whole 
stratum  might  at  last  be  drawn  together  into  a  lucid  spot  of  any 


('•'i',"«^'*flK?Mi,5g|0r»^.j:.j>',j;;. 


482 


A8TR0N0MT. 


W 


Mhape,  kceording  to  the  length,  breadth,  and  height  of  the  ntn- 
turn. 

"Riippoae  that  «  Hmaller  Mtnitum  pq  should  bninch  out  (mm 
the  former  in  >  certain  direction,  and  that  it  aluo  in  ronUinetl 
between  two  panllel  pluneii,  m>  that  the  eye  ia  conUin«!  <  within 
the  great  atratum  aomewhere  iDefore  the  aeparation,  and  not  far 
from  the  place  where  the  atraU  are  still  united.  I'hen  this  second 
Htratum  will  not  be  protected  into  a  bright  circle  like  the  former, 
but  it  will  be  seen  as  a  lucid  branch  proceeding  from  the  first,  and 
returning  into  it  again  at  a  diaUnoe  less  than  a  semicircle. 

"  In  the  figure  the  stars  in  the  small  stratum  p  q  will  be  pro- 
jected into  a  bright  uc  PRRP,  which,  after  ita  separation  from 
the  circle  C  B  D,  unitea  witii  it  again  at  P. 

"  If  the  bounding  aurfacea  are  not  parallel  planes,  but  irregularly 
curved  surfaces,  analogous  appearances  must  result." 

The  Milky  Way,  an  we  see  it,  preaents  the  aspect  which 
has  been  just  accounted  for,  in  ita  general  appearance  of  a 
girdle  around  the  heavens  and  in  its  bifurcation  at  a  cer- 
tain point,  and  Heksohel's  explanation  of  this  appear- 
ance, 88  just  given,  haa  never  been  seriously  questioned. 
One  doubtful  point  remains:  are  the  stars  in  Fig.  135 
scattered  all  through  the  space  S  —  abpdi  or  are  they 
near  its  bounding  planes,  or  clustered  in  any  way  within 
this  space  so  as  to  produce  the  same  result  to  the  eye  as  if 
uniformly  distributed  t 

Hbbsohel  assumed  that  they  wei-e  nearly  equably  ar- 
ranged all  through  the  space  in  question.  He  only  exam- 
ined one  other  arrangement — viz.,  that  of  a  ring  of  stars 
surrounding  the  sun,  and  he  pronounced  against  such  an 
arrangement,  for  the  reason  that  there  is  absolutely  noth- 
ing in  the  size  or  brilliancy  of  the  sun  to  cause  us  to  snp- 
{lose  it  to  be  the  centre  of  such  a  gigantic  system.  Mo 
reason  except  its  importance  to  us  personally  can  be  all^^ 
for  such  a  supposition.  By  the  assumptions  of  Fig.  186, 
each  star  will  have  its  own  appearance  of  a  galaxy  or  milky 
way,  which  will  vary  according  to  the  situation  of  the  star. 

Such  an  explanation  will  aooonnt  for  the  general  appear- 
ances of  the  Milky  Way  and  of  the  rest  of  the  sky,  sup- 
posing the  stars  equally  or  nearly  equally  distributed  in 
space.     On  this  supposition,  tlie  system  must  be  deeper 


d  height  of    the  ntn- 

)uld  branch  out  fioin 
t  it  aiRo  i»  contained 
fa  it  contains  I  within 
eparation,  and  nut  fitr 
led.  Then  this  Beconii 
circle  like  the  former, 
ling  from  the  first,  and 
a  femicircle. 
ratum  p  q  will  be  pro- 
ter  its  separation  from 

planes,  but  irregularly 
result." 

nts  the  aspect  whicli 
eral  appearance  of  a 
bifurcation  at  a  cer- 
ion  of  this  appear- 
Briousiy  questioned 
e  stars  in  Fig.  135 
ibpdi  or  are  they 
,  in  any  way  within 
Bsnlt  to  the  eye  as  if 

nearly  equably  ar- 
on.  He  only  exam- 
it  of  a  ring  of  stars 
ioed  against  such  an 
■e  is  absolutely  noth- 
in  to  cause  us  to  sup- 
Igantio  system.  No 
wnally  can  be  all^^ 
nptions  of  Fig.  136, 
of  a  galaxy  or  milky 
situation  of  the  star. 
>r  the  general  appear- 
rest  of  the  sky,  sup- 
jnally  distributed  in 
item  must  be  deeper 


BTRUGTURK  OF  THK  UK  A  VKIfS. 


where  the  stars  appear  more  niimorouH.  The  same  ovi- 
ilunce  can  be  strikingly  preouiitud  in  Hiiotliur  way  so  us  to 
include  the  renults  of  the  8f)Uthern  gauges  of  8ir  J<»hn 
IIkkhchel.  The  Galaxy,  or  Milky  Way,  being  nearly  a 
gnifii  circle  of  the  Hpliorc,  we  may  compute  the  position 
of  its  north  or  south  polo;  and  as  the  position  of  our  own 
))olar  points  can  evidently  Iiave  no  relation  to  the  stellar 
nnirene-,  we  express  the  position  of  the  gauges  in  galactio 
|)olar  dintance,  north  or  south.  By  subtracting  these 
polar  distances  from  90°,  we  shall  have  the  distance  of  each 
gauge  from  the  central  plane  of  the  Galaxy  itself,  the  stars 
near  90°  of  polar  disUuce  being  within  the  Galaxy.  The 
average  number  of  stars  per  Held  of  15'  for  each  zone  of 
15^  of  galactic  polar  distance  has  been  tabulated  by  Stbuve 
and  Hbbsohbl  as  follows: 


Zoom  or  Qalactto 

Ayanua  Namber 
of  Sun  per 

Zone*  of 

Average  Nunilier 

North  ruiar 

Oalactio  South  Polu 

of  Htara  per 
Field  of  ly. 

DIllMM. 

n«ld  of  My. 

DUtMce. 

0°  to  16' 

4-88 

0*   to  15° 

605 

1S°  to  80° 

843 

15°   to  80° 

66!) 

80°  to  45* 

881 

80°   to  45° 

908 

45°  t4.  60° 

18  01 

45°   to  60° 

18-49 

60°  to  78° 

2400 

80°  to  75° 

86-29 

75*  toW 

58-48 

75°  to  90° 

59-06 

This  table  clearly  shows  that  the  auperjioidl  distribution 
of  stars  from  the  first  to  the  fifteenth  magnitudes  over  the 
apparent  celestial  sphere  is  such  that  the  vast  majority  of 
them  are  in  that  zone  of  30°  wide,  which  includes  the 
Milky  Way.  Other  independent  researches  havt  shown 
that  the  fainter  lucid  stars,  considered  alone,  are  also  dis' 
tributed  in  greater  ntunber  in  tliis  zone. 

HsRsoan.  andeavored,  in  his  earhr  memoirs,  to  find  the  physical 
explanation  of  this  inequality  of  distribution  m  the  theory  of  the 
uniTerse  ezemplifled  in  Fig.  188,  which  was  based  on  the  funda- 
mental amumption  that,  on  the  whole,  the  otars  wen,  nearly  equably 
distributed  in  space. 


484 


ASTRONOMY. 


If  they  were  so  distributed,  then  the  number  of  stars  visible  in 
any  gauge  would  show  the  thickness  uf  the  stellar  system  in  the 
direction  in  which  the  telescope  was  pointed.  At  each  pointing, 
the  field  of  view  of  the  instrument  includes  all  the  visible  stars  sit- 
uated within  u  cone,  having  its  vertex  at  the  observer's  eye,  and  its 
base  at  the  vei7  limits  of  me  system,  the  angle  of  the  cone  (at  the 
eye)  being  IS'  4*.  Then  the  cubes  of  the  perpendiculars  let  fall 
from  the  eye  on  the  plane  of  the  bases  of  the  various  visiul  cones 
are  proiiortional  tj  the  solid  contents  of  the  cones  tliemselves,  or,  as 
the  stars  are  suppoaed  equally  scattered  within  all  the  cones,  the 
cube  roots  of  the  numbers  of  stars  in  each  of  the  fields  express  the 
relative  lengths  of  the  perpendiculars.  A  teetion  of  the  sidereal  sys- 
tem along  any  great  circle  can  thus  be  constructed  as  in  the  figure, 
which  is  copied  from  Hbbbchel. 

The  solar  system  is  supposed  to  bo  at  the  dot  within  the  mass  of 
stars.  From  this  point  fines  are  drawn  along  the  directions  in 
7'hich  the  gauging  telescope  was  pointed.  On  theae  lines  are  laid 
off  lengths  proportional  to  the  cube  roots  of  the  number  of  stars  in 
each  gauge. 


FlO.   186.— ABBAHOBMBNT   OF  THB  BTABS  ON   THB   HYP0THMI8  OF 
HQUABLB  DIflTRIBanON. 

The  irregular  line  joining  the  terminal  points  is  approximately 
the  bounding  curve  of  the  ^Uar  system  in  the  great  circle  chosen. 
Within  this  line  the  space  is  nearly  uniformly  filled  with  stars. 
Withov*  it  is  empty  space.  A  similar  section  can  be  constructed  in 
any  o.her  ^reat  circle,  joA  a  combination  of  all  such  would  give  a 
representation  of  the  shape  of  our  stellar  system.  The  more  numer- 
ous and  careful  the  observations,  the  more  elaborate  the  represen- 
tation, and  the  868  gauges  of  Hersohbl  are  sufilcient  to  mark  out 
with  great  precision  the  main  features  of  the  Milky  Way,  and  even 
to  indicate  some  of  its  chief  irregularities.  This  figure  may  be 
compared  with  Fig.  185. 

On  the  fundamental  assumption  of  Hbrbchbl  (equable  distribu- 
tion), no  other  conclusions  can  be  drawn  from  his  statistics  but 
that  drawn  by  him. 

This  assumption  he  subsequently  modified  in  some  desree,  and 
was  led  to  regard  his  gauges  as  indicating  not  so  much  the  depth 
uf  the  system  in  any  direction  as  the  clustering  power  or  tendency 
of  the  stars  in  those  special  regions.     It  is  clear  that  if  in  any 


r. 

number  of  stars  visible  in 
f  the  stellar  system  in  the 
pointed.  At  each  pointing, 
tides  all  the  visible  stars  sit- 
Eit  the  observer's  eye,  and  its 
:he  angle  of  the  cone  (at  the 
the  perpendiculars  let  fall 
of  the  various  visual  cones 
'  the  cones  themselves,  or,  as 
ed  within  all  the  cones,  the 
ach  of  the  fields  express  the 
A  teetion  of  the  sidereal  sys- 
sonstructed  as  in  the  figure, 

t  the  dot  within  the  mass  of 
wn  along  the  directions  in 
ed.  On  these  lines  are  laid 
>ta  of  the  number  of  stars  in 


STRUCTURE  OF  THE  HEAVENS. 


485 


m  ON   THR   HTPOTHmS  Or 
3TION. 

nal  points  is  approximately 
n  in  the  great  circle  chosen, 
iniformly  filled  with  stars. 
ectioD  can  be  constructed  in 
on  of  all  such  would  give  a 
r  system.  The  more  numer- 
aore  elaborate  the  repreaen- 
H<  are  sufficient  to  mark  out 
f  the  Millcy  Way,  and  even 
rities.     This  figure  may  be 

BRSCRBL  (equable  distribu- 
wn  from  his  statistics  but 

idifled  in  some  desree,  and 

ing  not  so  much  the  depth 

iistering  power  or  tendenr; 

It  is  clear  that  if  in  any 


given  part  of  the  sky,  where,  on  the  average,  there  are  10  stars 
(say)  to  a  field,  we  should  find  a  certain  small  portion  of  100  or 
more  to  a  field,  then,  on  Hgkhciiel's  first  hypothesis,  rigorously  in- 
terpreted, it  would  be  necessary  to  suppose  a  spike-shaped  protu- 
berance directed  from  the  earth  in  order  to  explain  the  increased 
number  of  stars.  If  many  such  places  could  on  found,  then  the 
probability  is  great  that  this  explanation  is  wiong.  We  should 
more  rationally  suppose  some  real  inequality  of  star  distribution 
here.  It  is,  in  fact,  in  just  such  details  that  the  system  of  Her- 
BCHEb  breaks  down,  and  the  careful «  xatnination  which  his  system 
has  received  leads  to  the  belief  that  it  must  be  greatly  modified  to 
cover  all  the  known  facts,  while  it  undoubtedly  has,  in  the  main,  a 
strong  basb. 

The  stars  are  certainly  not  uniformly  distributed,  and  any  gen- 
eral theory  of  the  sidereal  system  must  take  into  account  the  varied 
tendency  to  aggregation  in  various  parts  of  the  sky. 

The  curious  convolutions  of  the  Milky  Way,  observed  at  various 
parts  of  its  course,  seem  inconsistent  with  the  idea  of  verv  great 
depth  of  this  stratum,  and  Mr.  Pboctor  has  pointed  out  that  the 
circular  forms  of  the  two  "  coal-sacks"  of  the  Southern  Milky  Way 
indicate  that  they  are  really  i^obnlar,  instead  of  being  cvundric 
tunnels  of  great  length,  looking  into  space,  with  their  axes  directed 
toward  the  earth.  If  they  are  slobular,  then  the  depth  of  the 
Milky  Way  in  their  ndghborhood  cannot  be  greatly  dimrent  from 
their  diameters,  which  would  indicate  a  much  sualler  depth  than 
that  assigned  by  HEKscfueL. 

In  1817,  HBRscHBii  published  an  important  memoir  on  the  same 
subject,  in  which  his  firrt  method  was  largely  modified,  though 
not  abtuDdoned  entirely.  Itv  fuodamraital  j^ndple  was  stated  or 
him  as  follows : 

"  It  is  evident  that  we  cannot  mean  to  affirm  that  the  stars  of  the 
fifth,  sixth,  and  seventh  nuwnitudes  are  really  smaller  than  those 
of  the  first,  second,  or  third,  and  that  we  mustascrilM  the  cause 
of  the  difference  in  the  apparent  magnitudes  of  the  stars  to  a  differ- 
ence in  their  relative  diMancea  fnmi  us.  On  account  of  the  great 
number  of  stars  in  each  daas,  we  must  also  allow  that  the  star*  of 
each  succeeding  magniti^e,  Winning  with  the  first,  «re,  one  with 
another,  further  from  ns  than  thoae  of  the  masnitude  inunediately 
preceding.  The  relative  magnitudes  give  only  reUtive  distances, 
and  can  afford  no  information  as  to  the  real  distances  at  which  the 
stars  are  placed. 

"  A  stMidard  of  reference  for  the  arrangement  of  the  stars  may 
be  had  by  comparing  their  distribution  to  a  certain  properly  mod- 
ified equality  of  scattering.  The  equality  which  I  propoBe  does  not 
require  that  the  stars  should  foe  at  equal  distances  from  each  other, 
noi-  is  it  necessary  that  all  those  of  the  same  nominal  magnitude 
should  be  eqqallT  distant  from  us." 

It  consiBtsof  allotting  a  certain  equal  portion  of  space  to  every 
star,  so  that,  on  the  whole,  each  equal  portion  of  apace  within  the 
stellar  system  ccatains  an  equal  number  of  stars. 


486 


ASTRONOMT. 


The  space  about  each  star  can  be  ootuidered  spherical.  ^  8up> 
poM  such  a  sphere  to  lurround  our  own  san,  its  radius  will  not 

differ  greatly  from  the 
dirtance  of  the  nearest 
fixed  star,  and  this  is 
taken  as  the  unit  of 
distance. 

Suppose  a  series  of 
larger  spheres,  all 
drawn  around  our  sun 
as  a  centre,  and  having 
the  radii  8,  5,  7,  9, 
etc.  The  contents  of 
the  spheres  beinir  as 
the  cubes  of  their 
diameters,  the  first 
tphtrewIUhaTeS  x  8 
X  8  =  27  times  the 
volume  of  the  unit 
■phere,  and  will  there- 
fore be  latge  enough 
to  contain  87  stars ; 
tiie  second  will  have 
185  times  the  volume, 
•nd  will  therefore  con- 
tain 185  stars,  and  so 
with   the    successive 

teres.  The  figure 
ws  a  section  of 
portions  of  these 
(qiheres  ttp  to  that 
with  radius  11.  Above 
the  centre  are  given 
the  various  orders  of 
■tars  which  are  situ- 
ated between  the  sev- 
eral spheres,  while 
la  the  eerrespondin: 
•paces  below  the  cen- 
tre are  given  the  num- 
ber of  stars  which  the  rnrfon  is  large  enough  to  contain ;  for  in- 
stance, the  sphere  of  ramus  7  has  room  for  848  stan,  but  of  this 
space  185  puts  belong  to  the  spheres  inside  of  it :  there  is,  there- 
fore, room  for  818  stars  between  the  spheres  of  radii  8  and  7. 

^■■CBBi.  designates  the  several  distances .  of  these  lavers  of 
stars  as  orders  ;  the  stars  between  spheres  1  and  8  are  of  the  first 
order  of  distance,  those  between  8  and  5  of  the  second  order,  and 
so  on.  Comparing  the  room  for  stars  between  the  several  spliereB 
with  the  number  of  stars  of  the  several  magnitudes,  he  found  the 
result  to  be  as  follows : 


OP  SOTAIRSB  09  WttML 


STRUCTUBB  OF  THE  HEAVENS. 


487 


»iiHidered  spherical.  8up- 
II  ■un,  its  radius  will  not 
differ  greatly  inm  the 
dirtance  of  the  nearest 
llzed  star,  and  this  is 
taken  as  the  unit  of 
distance. 

Suppose  a  series  of 
larger  spheres,  all 
drawn  around  our  sun 
as  a  centre,  and  having 
the  radii  8,  6,  7,  9, 
etc.  The  contents  of 
the  spheres  beins  as 
the  cubes  of  their 
dUbmeters,  the  iirst 
■phirewlllhaTeS  x  8 
X  8  =s  S7  times  the 
Tolume  of  the  unit 
sphere,  and  will  there- 
fore be  latge  enough 
to  contidn  87  stars  ; 
the  second  will  have 
125  times  the  volume, 
and  will  therefore  con- 
tain ISS  stars,  and  so 
with  the  successive 
spheres.  The  figure 
snows  a  secUon  of 
portions  of  these 
■pheres  up  to  that 
with  radius  11.  Above 
the  centre  are  given 
the  various  orden  of 
■tars  whkh  an  situ- 
ated between  the  sev- 
eral spheres,  while 
in  tiie  oerrespondin : 
M,  spaces  below  the  cen- 
tre are  given  the  num- 
■ough  to  contain ;  for  in- 
i  for  848  Stan,  but  of  this 
ide  of  it :  then  is,  there- 
eres  of  radii  5  and  7. 
itances .  of  these  layen  of 
»  1  and  8  an  of  the  first 
of  the  second  order,  and 
tween  the  several  spheres 
magnitudes,  he  found  the 


Order  of  iMttnee. 

Number  of  Stars 
Uiere  la  Room  for. 

Xagnltade. 

Nambar  of  Stara 
ortbatMacnitada. 

1 

86 

98 

818 

896 

600 

866 

1,178 

1.588 

1 
8 

5 

5 
6 
7 

17 

2 

67 

8 

206 

4 

454 

5 

1,161 

6 

6,108 

7 

6,146 

8 

The  result  of  this  comparison  is,  that,  if  the  order  of  magnitudes 
could  indicate  the  distance  of  the  stars,  it  would  denote  at  first  a 
gradual  and  afterward  a  veij  abrupt  condensation  of  them. 

If,  on  the  ordinary  scale  of  magnitudes,  we  assume  thebrishtness 
of  any  star  to  be  inversely  proportional  to  the  sqiun  of  Its  dis- 
tance, it  leads  to  a  scale  of  distance  differant  from  that  adopted  by 
Hebbchei.,  so  that  a  rizth-magnitnde  star  on  the  common  scale 
would  be  about  of  the  eighth  order  of  distance  according  to  this 
scheme — that  is,  we  must  remove  a  star  of  the  first  magmtude  to 
eight  times  ita  actual  distance  to  make  it  shine  like  a  star  of  the 
sixth  magnitude. 

On  the  scheme  hen  laid  down,  Huwchbl  subsequently  assigned 
the  ordn*  of  distance  of  various  objects,  mostly  star-clusters,  and 
his  estimates  of  these  distances  an  still  quoted.  They  rest  on  the 
fundamental  hypothesis  which  has  been  explained,  and  the  error 
in  the  anumption  of  equal  brilliancv  for  all  stars,  affecto  these  esti- 
mates. It  is  perhaps  most  probable  that  the  hypothecs,  of  equal 
brillimcy  for  all  stan  is  still  mora  erroneous  ttuw  the  hypothesis 
of  equal  distribution,  and  it  may  well  be  ttat  th«e  is  a  verv  large 
range  indeed  in  tiie  aetoal  dimemdonsandin  the  intrinite  brilliaacy 
of  Stan  at  the  same  order  of  diataace  ftom  us,  so  that  the  tenth- 
magnitude  stars,  for  nample,  may  be  scattered  tbroiu^iout  the 
sphmres,  which  HnuinnD.  would  asdgn  to  tiie  seveiftfi,  eighth, 
nintii,  tenth,  eleventh,  twelfUi,  and  thirteenth  magnitudes. 

ESnee  the  tioM  of  HnnoMXL,  one  of  the  most  eimnent  of  the  as- 
tronomen  who  have  investigatodTthis  subject  is  STBimc  the  elder, 
formerly  director  of  the  Pulkowa  Observatonr.  His  reseanhes 
wen  founded  mainly  on  the  numben  of  stan  of  the  several  magni- 
tudes found  I^BnssL  in  a  zone  thirty  d^rees  wide  extending  all 
around  the  heavens,  15*  on  each  dide  of  the  equatw.  With  these 
he  eomUned  the  gauges  of  Sir  Willun  Hbrschbl.  The  hypothesis 
on  which  he  based  his  theory  was  rimilar  to  that  employed  by 
Hbbschbl  in  his  later  reseanhes,  in  so  far  that  he  supposed  the 
magnitude  of  the  stan  to  furnish,  on  the  average,  a  measura  of 
their  nlative  distances.  Supposing,  after  Hbbsohbl,  a  number  of 
concentric  spheres  to  be  drawn  around  the  mn  as  a  centra,  the  suc- 
cessive spaoea  between  •mtitSx  comsponded  to  stan  of  the  several 


488 


ASTRONOMY. 


maanitudea.  ho  found  that  the  further  out  he  went,  the  more  the 
8tlS  wore  condensed  in  and  near  the  Milky  Way.  This  concluston 
may  be  drawn  at  once  from  the  fact  we  have  ahready  mentioned, 
that  the  smaller  the  stars,  the  more  they  are  condensed  in  the  re- 
gion of  the  Galaxy.  ftniirrB  found  that  if  we  take  only  the  stare 
plainly  vUible  to  the  naked  eye-that  is.  th«»^«''"  *«  *>»«  *'*•* 
maimitude— they  are  no  thicker  in  the  Milky  Way  than  in  other 
parts  of  the  heavens.  But  those  of  the  sixth  magnitude  are  a 
little  thicker  in  that  region,  thoee  of  the  seventh  yet  thicker,  and 
soon,  the  inequality  of  distribution  becoming  constantly  greater  as 
the  telescopic  power  is  increased. 

From  all  this,  dntcvK  concluded  that  the  stellar  system  might 
be  considered  as  composed  of  layers  of  stars  of  various  densities,  all 
parallel  to  the  planeof  the  Milky  Way.  The  stars  are  thickest  in  wid 
hear  the  central  layer,  which  he  conceives  to  be  spread  out  as  a  wide, 
thin  sheet  of  stars.  Our  sun  is  ntuated  near  the  middle  of  this 
Uyer.  As  we  pass  out  of  this  layer,  on  either  side  we  find  the 
stars  constantly  growing  thinner  and  thinner,  but  we  do  not  reach 
any  distinct  boundary.  As,  if  we  could  riw  in  the  atmosphere,  we 
should  find  the  air  constantly  growUig  thinner,  but  at  m  gradual  a 
rate  of  progress  that  we  could  hardly  say  where  it  terminated  ;  so. 
on  arBuWa  view,  would  it  be  with  the  stellar  system,  if  we  could 
mount  up  in  a  direction  perpendicular  to  the  Milky  Way.  SrauvB 
gives  the  following  Uble  of  the  thickness  of  the  stars  on  each  side 
of  the  principal  plane,  the  unit  of  distance  being  that  of  the  ex- 
treme ^stance  to  which  HBBScBUi'B  telescope  could  penetrate  : 


Meu  DiitHiee 

betwvMi  Ndghbor- 

bagStan. 


In  the  principal  plane. . . . 

0-08  from  principal  piano 

010 

OW 

0-80 

0-40 

0-60 

OdO 

0-70 

0-80 

0-866 


10000 

0-48668 

0-88888 

0-88886 

017880 

018081 

006646 

006510 

008078 

001414 

0-C068S 


000 

87S 

458 

611 

778 

878 

861 

8-688 

8-180 

4-181 

0-788 


This  condensation  of  the  stars  near  the  central  plane  and  the 
gradual  thinnhig-out  on  each  dde  of  it  ate  onlyde^pied  to  be  the 
expression  of  the  general  or  average  distribution  of  those  bodies. 
The  probability  is  that  even  in  the  central  plane  the  stars  are  many 
times  as  thick  in  some  regions  as  in  others,  and  that,  as  we  tawe  the 
phme,  the  thimung-out  would  be  found  to  proceed  at  very  dmerent 
rates  in  different  regions.  That  there  may  be  a  gradual  thinning-out 


wmtum 


STRUCTURE  OF  THE  HEAVENa. 


489 


)  went,  the  more  the 
Fay.  This  conclusion 
e  already  mentioned, 
condensed  in  the  re- 
e  take  only  the  stars 
Me  down  to  the  fifth 
cy  Way  than  in  other 
ixth  magnitude  are  a 
enth  yet  thicker,  and 
;  constantly  greater  as 

stellar  system  might 
I  various  densities,  all 
ters  are  thickest  in  and 
e  sprmd  out  as  a  wide, 
«  the  middle  of  this 
her  side  we  find  the 
r,  but  we  do  not  reach 
in  the  atmosphere,  we 
ir,  but  at  so  gradual  a 
ere  it  termini^ed  ;  so, 
ar  system,  if  we  could 
Milky  Way.  Srauva 
the  stars  on  each  side 
wing  that  of  the  ex- 
le  could  penetrate : 


Mean  IMrtwee 

ingBian. 

1000 

R 

1279 

n 

1-468 

ff 

1011 

10 

irra 

1 

1-978      . 

Ml 

8-Ml 

0 

8-088 

V 

8-180 

4 

4-181 

a 

0-788 

central  plane  and  the 
>nly  designed  to  be  the 
ition  of  those  bodies, 
lane  the  stars  are  many 
nd  that,  as  we  leave  the 
poceed  at  very  different 
I  a  gradual  tlunnbg-out 


cannot  be  denied  ;  but  Strovb'b  attempt  to  form  a  table  of  it  is  open 
to  the  serious  objection  that,  like  HsRscHEti,  he  supposed  the  differ- 
ences between  the  magnitudes  of  the  stars  to  anse  entirely  from 
their  different  distances  from  us.  Although  where  the  scattering 
of  the  stars  is  nearly  uniform,  this  supposition  may  not  lead  us  into 
serious  error,  the  case  will  be  entirely  different  where  we  have  to 
deal  with  irregular  masses  of  stars,  and  especially  where  our  tele- 
scopes penetrate  to  the  boundary  of  the  stellar  system.  In  the 
latter  case  we  cannot  possibly  distinguish  between  small  stars  lying 
within  the  boundary  and  larger  ones  scattered  outside  of  it,  and 
Strutb's  gradual  thinning-out  of  the  stars  may  be  entirely  ac- 
counted for  by  great  diversities  in  the  absolute  brightness  of  the 
stars. 

Distribution  of  Stan.— The  brightness  B  of  any  star,  aa  seen 
from  tho  earth,  depends  upon  Im  surface  8,  the  intensity  of  its  light 
per  unit  of  sarfikce,  i,  and  its  distanoe  D,  so  that  its  brightneaa  can  be 
expressed  thus : 


for  another  star : 
and 


B       a-i 

B'   =.«'-<'• 

Nuw  this  ratio  of  the  brightness  B  4-  JS'  is  the  <mlj  fact  we  usually 
know  with  regard  to  any  two  stars.  D  has  been  determined  for 
only  a  few  Btara,  and  for  thetie  it  variaa  between  800,000  and  8.000,000 
times  the  major  axis  of  the  earth's  orbit.  8  and  i  are  not  known  for 
any  star.  There  la,  however,  a  prol>ability  that  t  does  not  vary  greatly 
from  star  to  star,  aa  the  gnat  majority  of  stars  are  white  in  color  (only 
some  700  red  stars,  for  instanoe,  are  known  out  of  the  300,000  which 
have  been  careftilly  examined).  Among  470  double  stars  of  Stbuvk's 
Hat  295  were  white,  08  being  bluish,  only  one  fourth,  or  118,  bdng 
yellow  or  red. 

If  JB  is  of  the  nth  mag.  ite  light  in  terms  of  a  first  magnitude  star 
is  4*  - 1  where  4  =  0- W7.  and  if  JSTIs  of  the  mth  mag.,  ite  light  is 
<>"-',  both  expressed  in  terms  of  the  lii^t  of  a  first  magnitude  star  aa 
unity  (J*  =  1). 

Therefore  we  may  put  J?  =  d»-',  5'  =  <J"-',  and  we  have 


=:  (la  —  ■>   — 


8 


jy* 


8'    iU^ 


D 


In  this  general  expression  we  seek  tlie  ratio  -j~ ,  and  we  have  it 

expressed  in  terms  of  four  unknown  quantities.    We  must  therefore 
make  some  supposition  in  regard  to  these. 

1.  Jf  M  ttar$  ore  of  equat  tHtrintie  britiianeif  and  of  equal  tke,  then 


8i,  iS*  <',  and  *•  --  s=  a  constant  =  -==-, 


•mmtmtm 


mmm 


hmh 


■  >  jrfjfl't*^ 


M.  j',Mf.vr)rg.w.v»u^jirrv<Jtr'ig; 


490 


A8TR0N0MT. 


whence  the  relative  distance  of  any  two  stan  would  be  known  on  this 
hypotheiila. 

II.  Or,  iuppote  the  itart  to  he  uniformly  diMr^mUd  in  »paee,  or  tiM 
■tar-densltjr  to  be  equal  in  all  directions.  From  this  we  can  also 
obtain  some  notions  of  the  relative  distances  of  stars. 

Call  Di,  Dt.D, D,  the  average  distances  of  stars  of  the 

1,  3,  8, nth  magnitudes. 

ir  K  stars  are  situated  within  the  sphere  of  radius  1,  then  the  num- 
ber of  stars  {Qn),  situated  within  the  sphere  of  radius  D.,  is 

since  the  cubic  contenta  of  spheres  are  as  the  cnlies  of  their  radii. 
Also 

«,_,  =  jr(D.-,)»,  i 

whence 


D,^ 


-V- 


«--« 


If  we  knew  Q,  and  Q»  - 1,  the  number  of  stan  contained  in  the 
spheres  of  radii  D%  and  D»  _  i,  then  the  ratio  of  D,  and  D»  -  i  would 
be  known.  We  cannot  know  Q.,  Q,  _  i,  etc.,  directly,  but  we  may 
suppose  these  quantities  to  be  proportional  to  the  numbera  of  stan  of 
the  nth  and  (n  —  l)tU  magnitudes  found  in  an  enumeration  of  all  the 
stare  in  the  heavens  of  these  magnitudes,  or,  lailinff  in  these  data,  we 
may  confine  this  enumeration  to  the  northern  liemispbere,  when 
LiTTROW  has  counted  the  number  of  stan  of  each  class  in  AReiLLAH- 
OBR's  Durehmuiterung.    As  we  have  seen  (p.  ti8) 


whence 


Q,  =  19,(»9  and  Q,  =  77,794, 
1>.    _  l/'Q^ 


^  -  i/  V'      - 
"2>,    ~  y    Q,    ~ 


1- 


and  this  would  lead  us  to  infer  that  the  stan  of  the  8th  magnitude 
were  distributed  inside  of  a  sphere  whose  radius  was  about  1  -6  times 
that  of  the  corresponding  sphere  for  the  7th  magnitiide  stars  provided 
that,  1st,  the  stara  in  general  are  equally  or  about  equally  distributed, 
and,  2d,  that  on  the  whole  the  stan  of  the  8  ....  »  magnitudes  are 

further  away  fh>m  us  than  thoae  of  the  7 (»  —  1)  munitudes. 

We  may  have  a  kind  of  test  of  the  truth  of  this  hypotSesis,  and  of 
the  fint  employed,  as  follows,  we  had : 


3b-i  -  y  0,-1 


Also  from  the  firat  hypothesis  the  briirhtnnas  S,  of  a  star  of  the  nth 
magnitude  in  terms  of  a  first  magnitude  star  =  1  was 

If  here,  again,  we  suppose  the  distance  of  a  fint  magnitude  star  to 
be  =  1  aira  of  an  nth  magnitude  star  !>..  then 


iiiMm»ii.ii).unu 


STRUCTURE  OF  THE  HEAVENS. 


491 


rould  be  known  on  this 

r^ttd  in  tpaee,  or  tho 

9*1001  thia  we  am  aleo 

ItAtn. 

■tanoes  of  aUrs  of  the 

radiua  1,  then  the  nam- 
radina  D»,  ia 


lie  cabea  of  their  r»dll. 


f  atara  contained  in  the 
of  Dn  and  D,  _  i  would 
.,  directly,  but  we  may 
the  numbera  of  atara  of 
enumeration  of  all  the 
lilinff  in  theae  data,  we 
urn  nemiaphere,  where 
ich  claaa  in  Abobllah- 
486) 

794. 


ra  of  the  8th  magnhnde 
ua  waa  about  1  -t  timea 
agnitude  atara  provided 
out  equally  diatributed, 
I ....  »  magnitndea  are 
(n  —  1)  munitudea. 
thia  hypotoeaia,  and  of 


Bm  of  a  Btar  of  the  nth 
=  1  waa 


llrat  waKnitnde  atar  to 


whence  ^;^  -  -^==- 

Comparing  the  expreaaion  for  ;g-^  >»  ^be  two  caaea,  we  have 

If  the  ▼alne  of  d  in  thia  laat  expreaaion  cmnea  near  to  the  value  which 
haa  been  deduced  for  it  from  direct  photometric  meaaurea  of  the 
relative  intenaity  of  varioua  claaaea  of  atara,  nia.,  i  =  0-40,  then  thia 
will  be  ao  far  an  argument  to  ahow  that  a  certain  amount  of  credence 
may  be  given  to  both  hypotheaea  I.  and  II.  Taking  the  valuea  of 
Q,  and  Q,,  we  hanre 

'<■•■'= (-^-)*=»*^ 

From  the  valuea  of  Q.  and  Qt,  there  reaulta  <)(•,  t)  =  0-45.  Theae, 
then,  agree  tolerably  well  with  the  independent  photometric  valuoa 
for  6,  and  ahow  that  the  equation 

givea  the  average  diatanee  of  the  atara  of  the  nth  magnitude  with  a 
certain  approach  to  aceuncy.  For  the  atan  from  lat  to  8th  magni- 
tude tiiaae  diatancea  are : 

1  to  1-9  nagaitnde. 100 

Sto9-9  ••  184 

8to8-9  "         «'88 

4to4-9  ••         8-84 

5to6-9  ••                 5-80 

8to8-9  "         8-81 

7  to  7-9  "         18-88 

8to8-9  •*         aO-88 

Thia  preaentaUon  of  the  anbjeet  ia  eaaentiidly  that  of  Prof.  Buoo 
GTLOni. 


!lllllilllll.Wlt.l|illl  JM     I 


timmmmxm ' 


. 


!'■> 


CHAPTER  VIII. 

COSMOGONY. 

A  THEOEY  of  the  operations  by  which  the  nmvewo  re- 
ceived its  present  form  and  arrangement  is  called  CTMmojy- 
my.  This  subject  does  not  treat  of  the  ongin  of  matter, 
but  only  with  its  transformations. 

Threi  systems  of  Cosmogony  have  prevailed  among 
thinking  men  at  different  times. 

(1.)  That  the  universe  had  no  origin,  but  existed  from 
eternity  in  the  form  in  which  we  now  sec  It. 

(2.)  That  it  was  created  in  ito  present  shape  m  a 
moment,  out  of  nothing. 

(8.)  That  it  came  into  its  present  form  through  an  ar- 
rangement of  materials  which  were  before  "  without  form 

"""TheU  seems  to  be  thoidea  which  has  most  prevailed 
among  thinking  men,  and  it  receives  many  ^tnlong  con- 
firmations from  the  scientific  discoveries  of  modem  times. 
^Z  Utter  seem  to  show  beyond  aU  "-TJ^^  .^^^ 
the  universe  could  not  always  have  existed  mits  present 
S^rdi::?deritspresentconditions;ih.ttherew..at^^ 

when  the  materials  composing  it  were  masses  of  glowing 
vapor,  and  that  there  will  be  a  time  when  the  present  state 
of  things  wiU  cease.  The  explanation  of  the  procewes 
through  which  this  occurs  is  sometimes  called  the  nefttjtor 
AvpoSm*.  It  was  first  propounded  by  the  philosopben 
SwBDE^BOBO,  Kant,  and  Laplace,  and  although  since 
greatly  modified  in  detail,  the  views  of  these  men  have  m 
tiie  main  been  retained  until  the  present  time. 


C08M0G0NT. 


408 


[. 


I  the  tmiverwre- 
c  is  called  Coanwg- 
j  origin  of  matter, 

prevailed   among 

,  bnt  existed  from 

ee  it. 

Bsent   shape   in  a 

rm  through  an  ar- 
)re  "  without  form 

has  most  prevailed 
many  striking  con- 
BB  of  modem  times, 
isonable  doubt  that 
asted  in  its  present 
;hat  there  waa  a  time 
masses  of  glowing 
len  the  present  state 
m  of  the  processes 
IS  called  the  ndnilar 
Dy  the  philosophers 
und  although  since 
f  these  men  have  in 
mt  time. 


Wo  eliall '.  n  its  consideration  by  a  statement  of  the 
various  facts  which  appear  to  show  that  the  earth  and 
planets,  as  well  as  the  sun,  were  once  a  fiery  mass. 

The  first  of  these  facts  is  the  g^dual  but  uniform  in- 
crease  of  temperature  as  we  descend  into  the  interior  of 
the  earth.  Wherever  mines  have  been  dug  or  wells  sunk 
to  a  great  depth,  it  is  found  that  the  temperature  increases 
as  we  go  downward  at  the  rate  of  about  oite  degree  centi- 
grade to  every  30  metres,  or  one  degree  Fahrenheit  to 
every  50  feet.  The  rate  differs  in  different  places,  bnt  tlie 
general  average  is  near  this.  The  conclusion  which  we 
draw  from  this  may  not  at  first  sight  be  obvious,  because 
it  may  seem  that  the  earth  might  always  have  shown  this 
same  increase  of  temperature.  But  there  are  several  re- 
suits  which  a  little  thought  will  make  clear,  although  their 
complete  establishment  requires  the  use  of  the  higher 
mathematics. 

The  first  result  is  that  the  increase  of  temperature  ean- 
not  be  merely  superficial,  but  must  extend  to  a  great 
depth,  probably  even  to  the  centre  of  the  earth.  If  it  did 
not  so  extend,  the  heat  would  have  all  been  lost  long  ages 
ago  by  conduction  to  the  interior  and  by  radiation  from 
the  surface.  It  is  certain  that  the  earth  has  not  received 
any  great  supply  of  heat  from  outside  since  the  earliest 
geological  ages,  because  such  an  accession  of  heat  at  the 
earth's  surface  would  have  destroyed  all  life,  and  even 
melted  all  the  rocks.  Therefore,  whatever  heat  there  is 
in  the  interior  of  the  earth  must  have  been  there  from  be- 
fore the  commencement  of  life  on  the  globe,  and  rwnained 
through  all  geological  ages. 

The  interior  of  the  earth  being  hotter  than  its  surface, 
and  hotter  than  the  spacearoundit,  must  be  losing  heat. 
We  know  by  the  most  familiar  observation  that  if  any  ob- 
ject is  hot  inade,  the  heat  will  work  its  way  through  to  the 
surface  by  the  process  of  conduction.  Therefore,  since  the 
earth  is  a  great  deal  hotter  at  the  depth  of  30  metres  than 
it  is  at  the  surface,  heat  must  be  continually  coming  to  the 


■?.<^?»>»i,'fW™qyi,-^:_^?^--  > 


494 


ABTRONOMT. 


4 


Burfaoe.  On  reaching  the  surface,  it  muBt  be  radiated  off 
into  space,  else  the  surface  would  have  long  ago  become 
as  hot  as  the  interior.  Moreover,  this  Iobb  of  heat  must 
have  been  going  on  since  the  beginning,  or,  at  least,  since 
a  time  when  the  surface  was  as  hot  as  the  interior.  Thus,  if 
we  recffbn  backward  in  time,  we  find  tliat  there  must  have 
been  vaote  and  more  heat  in  the  earth  the  further  back 
we  go,  so  that  Ve  must  finally  reach  back  to  a  time  when 
it  was  so  hot  as  to  be  molten,  and  then  again  to  a  time 
when  it  was  so  hot  as  to  be  a  mass  of  fiery  vapor. 

The  second  fact  is  that  we  find  the  son  to  be  cooling  off 
like  the  earth,  only  at  an  incomparably  more  rapid  rate. 
The  sun  is  constantly  radiating  heat  into  space,  and,  so  far 
as  we  can  ascertain,  receiving  none  back  again.  A  snudl 
portion  of  this  heat  reaches  the  earth,  and  on  this  portion 
depends  the  existence  of  life  aud  motion  on  the  earth's  sur- 
face. The  quantity  of  heat  which  strikeB  the  earth  is  only 
'^'^'>^  hiiAmsi  o^  ^^  which  the  sun  radiatCB.  This 
fraction!  eipresBes  the  ratio  of  the  apparent  surface  of  the 
eart)l,  as  seen  from  the  sun,  to  that  of  the  whole  celestial 
sphere. 

Since  the  son  is  losing  heat  at  this  rate,  it  must  have  had 
more  heat  yesterday  than  it  has  to-day  ;  more  two  days  ago 
than  it  had  yesterday,  and  so  on.  Thus  calcuUting  back- 
ward, we  find  that  tiie  further  we  go  back  into  time  the 
hotter  the  sun  must  have  been.  Since  we  know  that  heat 
expands  all  bodies,  it  follows  that  the  sun  must  have  been 
larger  in  past  agee  than  it  is  now,  and  we  can  trace  back 
this  increase  in  size  without  limit.  Thus  we  are  led  to  the 
conclusion  that  there  must  have  been  a  time  when  the  sun 
filled  up  the  space  now  occupied  by  the  planets,  and  must 
have  been  a  very  rare  mass  of  glowing  vapor.  The  plan- 
ets could  not  then  have  existed  separately,  but  must  have 
formed  a  part  of  this  mass  of  vapor. '  The  latter  was  there- 
fore the  material  out  of  which  the  kAmx  system  was 
formed. 

The  aame  process  maybe  continued  into  the  future. 


■BBW 


<y< 


iBt  bo  radiated  off 
long  ago  become 
MB  of  heat  must 
or,  at  least,  since 
interior.  Thus,  if 
it  there  must  have 
the  farther  back 
ik  to  a  time  when 
t  again  to  a  time 
ry  vapor. 

n  to  be  cooling  off 
more  rapid  rate. 
I  space,  and,  so  far 
t  again.  A  small 
nd  on  this  portion 
on  the  earth's  sor- 
es the  earth  is  only 
m  radiates.  This 
•ent  surface  of  the 
the  whole  celestial 

I),  it  must  Iwye  had 
more  two  days  ago 
m  calculating  back- 
jack  into  time  the 
we  know  that  heat 
in  must  have  been 
we  can  trace  back 
us  we  are  led  to  the 
,time  when  the  sun 
e  planets,  uidmust 
vapor.    Theplan- 
tely,  but  must  have 
Sie  latter  was  there- 
BoHu  system  waa 

ed  into  the  future. 


Since  the  sun  by  its  radiatioa  li  sonstantlj  ,^>dng  heat,  it 
must  grow  cooler  and  cooler  as  ttge^  advi««wie,  and  must 
finally  radiate  so  little  heat  that  life  and  motion  can  no 
longer  exist  on  our  globe. 

The  third  fact  is  that  the  revolutions  of  all  the  planets 
around  the  sun  take  place  in  the  same  direction  and  in 
nearly  the  same  plane.  We  have  hero  a  similarity  amongst 
the  different  bodies  of  the  solar  system,  wfiioh  must  have 
had  an  adequate  cause,  and  the  only  cause  which  has  ever 
been  assigned  is  found  in  the  nebular  hypothesis.  This 
hypothesis  supposes  that  the  sun  and  planets  were  once 
a  great  mass  of  vapor,  as  large  as  the  present  solar  system, 
revolving  on  its  axis  in  the  same  plane  in  which  the 
planets  now  revolve. 

The  fourth  fact  is  seen  in  the  existence  of  nebulas.  We 
have  already  stated  that  the  spectroscope  shows  these  bodies 
to  be  masses  of  glowing  vapor.  We  thus  actually  see  mat- 
ter in  the  celestial  spaces,  under  the  very  form  in  which 
the  nebular  hypothesis  supposes  the  matter  of  our  solar 
system  to  have  once  existed.  Sinoe  these  masses  of  vapor 
are  so  hot  as  to  radiate  light  and  heat  through  the  immense 
distance  which  separates  us  from  them,  they  most  be  grad- 
ually cooling  off.  This  cooling  must  at  lengUi  reach  a 
point  when  they  will  cease  to  be  vaporous  and  condense 
into  6bjects  Hke  stars  and  planets.  We  know  that  every 
star  in  the  heavens  radiates  heat  as  our  sun  does.  In  the 
case  of  the  brighter  stars  the  heat  radiated  has  been  made 
sendble  in  the  f  od  of  our  telescopes  by  means  of  the  thermo- 
multiplier.  The  general  relation  which  we  know  to  ex- 
ist between  light  and  radiated  heat  shows  that  all  the  stars 
must,  like  the  sun,  be  radiating  heat  into  spaoe. 

A  fifth  fact  is  afforded  by  Ae  physical  constitution  of 
the  planets  Jupiter  and  Saturn.  The  tetoscopie  examina. 
tion  of  tiiese  planets  shows  that  changes  on  their  surfaces 
are  constantly  going  on  with  a  rapidity  and  violence  to 
which  nothing  on  the  surface  of  our  earth  can  compare. 
Such  operations  can  be  kept  up  only  through  the  ^ncy  of 


.«..- 


ABTRoyonr. 


heat  or  some  equivalent  furiu  uf  energy.  But  at  the  dis. 
tance  of  Jupiter  and  Sntum  the  rayn  of  the  sun  are  entirely 
insufficient  to  produce  changes  so  violent.  Wo  are  there- 
fore led  to  infer  that  Jupiter  and  Saturn  must  be  hot 
bodies,  and  must  therefore  be  cooling  off  like  the  sun, 
stars  and  earth. 

We  are  tlius  led  to  tJie  general  conclusion  that,  so  far 
as  our  knowledge  oxtend^,  nearly  all  the  bodies  of  the 
universe  are  hot,  and  are  cooling  off  by  radiating  their 
heat  into  space.  Before  the  discovery  of  the  "  conserva- 
tion of  energy,"  it  was  not  known  that  this  radiation  in- 
volv«)d  the  waste  of  a  something  which  is  necessarily  Umited 
in  supply.  But  it  is  now  known  that  heat,  motion,  and 
other  forms  of  force  are  to  a  certain  extent  convertible  into 
each  other,  and  admit  of  being  expressed  as  quantities  of 
a  general  something  which  is  called  energy.  We  may  de- 
fine the  unit  of  energy  in  two  or  more  ways  :  as  the  quan- 
tity which  is  required  to  raise  a  certain  weight  through  a 
certain  height  at  the  surface  of  the  earth,  or  to  heat  a  given 
quantity  of  water  to  a  certain  temperature.  However 
we  express  it,  wr  know  by  the  laws  of  matter  that  a  given 
mass  of  matter  can  contain  only  a  certain  definite  number 
of  units  of  energy.  When  a  mass  of  matter  either  gives 
off  heat,  or  causes  motion  in  other  bodies,  we  know  that 
its  energy  is  being  expended.  Since  the  total  quantity  of 
energy  which  it  contains  is  finite,  the  process  of  radiating 
heat  must  at  length  come  to  an  end. 

It  is  sometimes  supposed  thi^  this  cooling  off  may  be 
merely  a  temporary  process,  and  that  in  time  something 
may  happen  by  which  all  the  bodies  of  the  oniverse  will 
receive  back  again  the  heat  which  they  have  lost.  This  is 
founded  upon  the  general  idea  of  a  oompensating  process  in 
nature.  As  a  special  example  of  its  application,  some  have 
supposed  that  the  planets  may  ultimately  fall  into  the  sun, 
and  thus  generate  so  much  heat  as  to  reduce  the  snn  once 
m<Mre  to  vapor.  All  these  theories  are  in  direct  opposition 
to  the  well-establiahed  laws  of  heat,  and  can  be  justified 


But  at  the  diB< 
i  sun  are  entirely 

We  are  there- 
tm  must  be  hot 
)S  like  the  sun, 

uion  that,  so  far 
le  bodies  of  the 
»y  radiating  their 
f  the  "  conserva- 
this  radiation  in- 
leoessarily  limited 
lieat,  motion,  and 
it  convertible  into 
d  as  quantities  of 
^.     We  may  de- 
rays  :  as  the  quan- 
weight  through  a 
,  or  to  heat  a  given 
rature.     However 
latter  that  a  given 
n  definite  number 
latter  either  gives 
ies,  we  know  that 
e  total  quantity  of 
rocesB  of  radiating 

ooling  off  may  be 
in  time  something 
I  the  universe  will 
have  lost.  This  is 
)en8ating  process  in 
lication,  some  have 
ly  fall  into  the  sun, 
educe  the  sun  once 
in  direct  opposition 
d  can  be  justified 


COSMOGONT. 


407 


only  by  fioine  gcnoralizutiun  which  Hhall  Im3  fur  wider  than 
any  that  science  has  yet  reached.  Until  we  have  bucIi  a 
goneralizatiou,  every  such  theory  founded  upon  or  consist- 
ent with  the  laws  of  nature  is  a  neceosary  failure.  All  the 
heat  that  could  be  generated  by  a  fall  of  all  the  planets  into 
the  sun  would  not  produce  any  change  in  its  constitution, 
and  would  only  last  a  few  years.  The  idea  that  the  heat 
radiated  by  the  sun  and  stan  may  in  some  way  Ik)  collected 
and  returned  to  them  by  the  mere  operation  of  natural  laws 
is  equally  untenable.  It  is  a  fundamental  principle  of  the 
laws  of  heat  that  the  latter  can  never  pass  from  a  cooler 
to  a  warmer  body,  and  that  a  l>ody  can  nevor  grow  warm 
or  acquire  heat  in  a  space  that  is  cooler  .nan  the  body  is 
itself.  All  diiferences  of  temperature  tend  to  equalize 
themselves,  and  the  only  state  of  things  to  which  the  uni- 
verse can  tend,  under  its  present  laws,  is  one  in  which  all 
space  and  all  the  bodies  contained  in  space  are  at  a  uniform 
temperature,  and  then  all  motion  and  change  of  tempera- 
ture, and  hence  the  conditions  of  vitality,  mtifct  cease.  And 
then  all  such  life  as  ours  must  cease  also  unless  sustained 
by  entirely  new  methods. 

The  general  result  drawn  from  all  these  laws  and  facts 
is,  that  there  was  once  a  time  when  all  the  bodies  of  the 
universe  formed  either  a  single  mass  or  a  number  of  masses 
of  fiery  vapor,  having  slight  motions  in  various  parts,  and 
different  degrees  of  density  in  different  regions.  A  grad- 
ual condensation  around  the  centres  of  greatest  density  then 
went  on  in  consequence  of  the  cooling  and  the  mutual  at- 
traction of  the  parts,  and  thus  arose  a  great  number  of 
nebulous  masses.  One  of  these  masses  formed  the  ma- 
terial out  of  which  the  sun  and  planets  are  supposed  to 
have  been  formed.  It  was  probably  at  first  nearly  glob- 
ular, of  nearly  equal  density  throughout,  and  endowed 
with  a  very  slow  rotation  in  the  direction  in  which  the 
planets  now  move.  As  it  cooled  off,  it  grew  smaller  and 
smaller,  and  its  velocity  of  rotation  increased  in  rapidity  by 
virtue  of  a  well-established  law  of  mechanics,  known  a* 


?j»!rs*-,SS»«- 


'"v 


.'11 


II 


498 


ABTRONOMT. 


that  of  the  conservation  qf  curecm.  According  to  tliis  law, 
whenever  a  eystem  of  particles  of  any  kind  whatever,  which 
is  rotating  around  an  axis,  changes  its  form  or  arrangement 
by  virtue  of  the  mutual  attractions  of  its  parts  among  them- 
selves, the  sum  of  all  the  areas  described  by  each  particle 
around  the  centre  of  rotation  in  any  unit  of  time  remains 
constant.     This  sum  is  called  the  areolar  vdoeity. 

If  the  diameter  of  the  mass  is  reduced  to  one  half,  sup- 
posing it  to  remain  spherical,  the  area  of  any  plane  passing 
through  its  centre  will  be  reduced  to  one  fourth,  because 
areas  are  in  proportion  to  the  square  of  the  diameters. 
In  order  that  the  areolar  velocity  may  then  be  the  same 
as  before,  the  mass  must  rotate  four  times  as  fast.  The 
rotating  mass  we  have  described  must  have  had  an  axis 
around  which  it  rotated,  and  therefore  an  equator  defined 
as  being  everywhere  90°  from  this  axis.  In  consequence 
of  the  increase  in  the  velocity  of  rotation,  the  centrifugal 
force  would  also  be  increased  as  the  mass  grew  smaller. 
This  force  varies  as  the  radius  of  the  circle  described  by 
the  particle  multiplied  by  the  square  of  the  angular  velocity. 
Hence  when  the  masses,  being  reduced  to  half  the  radius, 
rotate  four  times  as  fast,  the  centrifugal  force  at  the  equa- 
tor would  be  increased  i  X  4*,  or  eight  times.  The  gravi- 
tation of  the  mass  at  the  surface,  being  inversely  as  the 
square  of  the  distance  from  the  centre,  or  of  the  radius, 
would  be  increased  four  times.  Therefore  as  the  masses 
continue  to  contract,  the  oentrifogal  force  increases  at  a 
more  rajad  rate  than  the  oentoal  attraction.  A  time  would 
therefore  come  when  they  would  balance  each  other  at  the 
equator  of  the  mass.  The  mass  would  then  oease  to  con- 
tract at  the  equator,  but  at  the  poles  time  would  be  no 
centoifugal  force,  and  the  gravitation  of  the  mass  would 
grow  stronger  and  stronger.  In  consequence  the  mass  would 
at  length  assume  the  form  of  a  lens  or  disk  very  thin  in  pro- 
portion to  its  extent.  The  denser  portions  of  this  lens 
would  gradually  be  inlwn  toward  the  centre,  and  there 
more  o^  less  solidified  by  tiie  process  of  cooling.    A  point 


-«■ 


COSMOGONY. 


499 


sordingto  tluB  law, 
id  whatever,  which 
rm  or  arrangement 
parts  among  them- 
id  by  each  particle 
it  of  time  remains 

A  to  one  half,  sup- 
f  any  plane  passing 
>ne  fourth,  because 
of  the  diameters, 
y  then  be  the  same 
imes  as  fast.     The 
b  have  had  an  axis 
an  equator  defined 
I.     In  consequence 
on,  the  centrifugal 
mass  grew  smaller, 
circle  described  by 
he  angular  velocity. 
I  to  half  the  radius, 
1  force  at  the  equa- 
times.    The  gravi- 
ing  inversely  as  the 
,  or  of  the  radius, 
ef  ore  as  the  masses 
force  inereases  at  a 
ion.    A  time  would 
loeeaoh  other  at  the 
i  then  cease  to  oon- 
thwe  would  be  no 
of  the  mass  would 
lenoe  the  mass  would 
[ilk  very  thin  in  pro- 
ortions  of  this  lens 
he  centre,  and  there 
)f  cooling.    A  point 


would  at  length  be  reached,  when  solid  particles  would  begin 
to  be  formed  throughout  the  whole  disk.  These  would  grad- 
ually condense  around  each  other  and  form  a  single  planet,or 
they  might  break  up  into  small  masses  and  form  a  group  of 
planets.  As  the  motion  of  rotation  would  not  be  altered 
by  these  processes  of  condensatioa,  these  pknets  would  all 
be  rotating  around  the  central  part  of  the  mass,  which  is 
supposed  to  have  condensed  into  the  sun. 

It  is  supposed  that  at  first  these  planetary  masses,  being 
very  hot,  were  composed  of  a  central  mass  of  those  sub- 
stances which  condensed  at  a  very  high  tranperatore,  sur- 
rounded by  the  vapors  of  those  substances  which  were 
more  volatile.  We  know,  for  instance,  that  it  takes  a  much 
higher  temperature  to  reduce  lime  and  platinum  to  vapor 
than  it  does  to  reduce  iron,  zinc,  or  magnesium.  There- 
fore, in  the  original  planets,  the  limes  and  earths  would 
condense  first,  while  many  other  metals  would  still  be  in  a 
state  of  vapor.  The  planetary  masses  would  each  be 
affected  by  a  rotation  increasing  in  rapidity  as  they  grew 
smaller,  and  would  at  length  form  masses  of  melted  metals 
and  vapors  in  the  same  way  as  the  larger  nuss  out  of  which 
the  sun  and  planets  were  formed.  These  masses  would 
then  condense  into  a  planet,  with  satellites  revolving 
around  it,  just  as  the  original  mass  condensed  into  sun  and 
planets. 

At  first  the  ]danet8  would  be  so  hot  as  to  be  in  a  molten 
condition,  each  of  them  probably  shining  like  the  son. 
They  would,  however,  slowly  cool  off  by  the  radiation  of 
heat  from  their  surf aoes.  So  long  as  they  remained  liquid, 
the  surface,  as  fast  as  it  grbw  oocd,  would  sink  into  the  in- 
terior on  aooonnt  of  its  greater  specific  gravity,  and  its 
place  would  be  taken  by  hotter  material  rising  from  the 
interior  to  the  surface,  there  to  cool  off  in  its  turn.  There 
would,  in  fact,  be  a  motion  sometiiing  like  that  whidb  occurs 
whoi  a  pot  of  cold  watw  is  set  upon  the  fire  to  boil. 
Whenever  a  mass  of  water  at  the  bottom  of  the  pot  is 
heated,  it  rises  to  the  surface,  and  (he  co<4  water  moves 


HmgWWMWJMWHWBtfii 


^H'iepN^f^miRsitmm'm^e^mt'^ 


500 


ASTBONOMT. 


P 


down  to  take  its  place.  Thus,  on  the  who  e,  m  long  as 
the  phinet  ,«maiSed  liquid,  it  ^ould  <K)ol  off  «jn^y 
throughout  its  whole  mass,  owing  to  the  conrtant  motion 
from  the  centre  to  the  cL-cumferenoe  and  back  again  A 
time  would  at  length  arrive  when  many  of  the  earths  and 
mXlTwouldbegirtosolidify.  At  first  the  solid  particles 
would  be  carried  up  and  down  with  the  liquid.  A  time 
would  finaUy  arrive  when  they  would  become  so  large 
and  nmneious,  and  the  liquid  part  <>**»»«  8«r[»»  "T 
become  so  viscid,  that  the  motion  would  be  obstructed. 
The  planet  would  then  begin  to  solidify.  Jwo  J^ews 
have  been  entertained  respecting  the  process  of  solidifica- 

*Tccording  t»>  one  view,  the  wtole  surface  of  the  planet 
would  solidify  into  a  continuous  crust,  as  ice  forms  over  a 
pond  in  cold  weather,  while  the  interior  was  still  m  a 
molten  state.  The  interior  liquid  could  Oien  no  longer 
come  to  the  surface  to  cool  off,  and  could  lose  no  heat 
except  what  was  conducted  through  this  crust  Hence 
the  subsequent  cooHng  would  be  much  slower,  and  the 
Klobe  would  long  remain  a  mass  of  lava,  covered  over  by 
a  comparatively  thin  soUd  crust  like  that  on  which  we 

livQ 

The  other  view  is  that,  when  the  cooling  attoined  a  cer- 
tain  stage,  the  central  portion  of  the  globe  would  be 
solidified  by  the  enormous  pressure  of  ^«  f  P«™^"J?"' 
portions,  while  the  exterior  was  stiU  flmd,  and  that  thus 
Sie  soUdification  would  take  pUM»  from  the  centre  out- 

ward. 

It  is  still  an  unsettled  question  whether  the  earth  is  now 
soUd  to  its  centre,  or  whether  it  is  a  great  globe  of  molten 
matter  with  a  comparatively  thin  crust  Astronomers  and 
physicists  incline  to  the  former  view  ;  geologisto  to  the 
ktter  one.  Whichever  view  may  be  correct,  it  appears 
certain  that  there  are  great  hikes  of  bva  in  the  interior 
from  which  volcanoes  are  fed.  ^ 

It  must  be  understood  that  the  nebukr  hypothesis,  as 


COBMOOONT. 


601 


I  whole,  so  long  as 
1  cool  off  equally 
ihe  constant  motion 
ind  back  again.  A 
y  of  the  earths  and 
(t  the  solid  particles 
(he  liquid.  A  time 
Id  become  so  large 
>f  the  general  mass 
raid  be  obstmeted. 
lidify.  Two  views 
process  of  solidifica- 

nrfaoe  of  the  planet 
,  as  ice  forms  over  a 
terior  was  still  in  a 
onld  then  no  longer 
,  could  lose  no  heat 
this  crust  Hence 
uch  slower,  and  the 
iva,  covered  over  by 
9  that  on  which  we 

ooling  attained  a  cer- 
the  globe  would  be 
I  the  superincumbent 
1  fluid,  and  that  thus 
Ennn  the  centre  out- 

jther  the  earth  is  now 
gi«at  globe  of  molten 
»t  Astronomers  and 
w  ;  geologistB  to  the 
be  correct,  it  appears 
I  htvain  die  interior 

lebnlar  hypothesis,  as 


we  have  explained  it,  is  not  a  perfectly  established  scien- 
tific theory,  but  only  a  philosophical  conclusion  founded 
on  the  widest  study  of  nature,  and  pointed  to  by  many 
otherwise  disconnected  facts.  The  widest  generalization 
associated  with  it  is  that,  so  far  as  we  can  see,  the  universe 
is  not  self-sustMuing,  but  is  a  kind  of  organism  which,  like 
all  other  organisms  we  know  of,  must  come  to  an  end  in 
consequence  of  those  very  laws  of  action  which  keep  it 
going.  It  must  have  had  a  beginning  within  a  certain 
number  of  years  which  we  cannot  yet  calculate  with  cer- 
tainty, but  which  cannot  much  exceed  20,000,000,  and  it 
must  end  in  a  diaos  of  cold,  dead  globes  at  a  calculable 
time  in  the  future,  when  the  sun  and  stars  shall  have 
radiated  away  all  their  heat,  unless  it  is  re-created  by  the 
action  of  forces  of  which  we  at  present  know  nothing. 


liiiiwili 


ns,  IB 


ram. 


'<mmumiumi^>mmm>mmuiit».f!»».r-  a^Mw., 


•  jawawM'-t  '^MfUn^SMUnUW 


ii.'.IUi.iiim.'MilltWi.'MM 


INDEX. 


GV  Tan  index  is  intended  to  point  out  the  subjects  treated  in  the 
work,  and  f  urtlier,  to  give  references  to  the  pages  where  technical  terms 
are  defined  or  explained. 


Abemtion'Oonstant,    values    of, 

944. 
Aberration  of  a  lens  (chromatic), 

60. 
Aberration  of  a   lens  (q>herical), 

61. 
Aberration  of  light.  888. 
Absolute  paralkx  of  stars  defined, 

476. 
Aooelerating  force  defined,  140. 
Achromatic  teleaoc^  described, 

60. 
ADAin'i  work  on  pettariMtkMis  of 

Ufamia,8M. 
AflJaataMntt  of  a  tiansit  fautra- 

ment  an  three ;  tot  level,  for 

ooOtmatkn,  and  for  aiimath,  77. 
AeroUtea^  87S. 
Aibt'b  dstenninntkm  of  the  denri> 

ty  of  the  earth.  IM. 
Algol  (variaUe  ataiX  440. 
Altitude  of  a  star  deOned.  M. 
Annnhv  mlUifaat  of  the  sob,  17&, 
AottBUMl  eqafaun,  110. 
Appannt  piMe  of  a  star,  985. 
Appamt  Mml-41«BMier  of  a  oeles- 

tMbo47deaaMl.09. 
Appnaot  thae,  9rj0. 
ABAAo'a  catalogoe  of  Aeralites, 

87S. 
Arc  conwlod  into  ttaaa^  89. 


Arsblaiidbb's  DurefamuatCTung, 
48S. 

Aboblamubr's  uranometiy,  48S. 

ARUTABCHm  detmnines  tlie  solar 
parsllak,  988. 

Abiitabchub  maintains  the  rota- 
tion of  the  earth.  14. 

Artificial  horiion  used  with  sex- 
tant on  shore.  95. 

Aspects  of  the  pknets.  979. 

Aann'a.  voir,  computation  of 
orMt  of  Dooati's  comet,  400. 

Asteroids  defined.  968. 

Asteralda,  Bomber  of,  900  in  187B, 
841. 

Aatenida.  their  magnitudes.  841. 

Afltronomkal  fautrumenta  (hi  gen- 
eral), 68. 

AstranomieBl  onita  of  lei^ith  and 
mass,  914. 

AatmioBij  (defined).  1. 

Atmoaphsfe  of  the  mooa,  881. 

Atmoaphena  of  the  phuets,  «• 
Iteauy,  Venus,  eto. 

Axia  of  flie  oelesttat  ^ihera  da- 
fiBed.98. 

Axis  of  th' ^arth  defiBBd.  96. 

AifaBoth  Tof  a  tnuiBtt  bislro- 
meat.  77. 

BAiLT'a  datermbiatioD  at  the  den- 
s^jr  of  the  eartt.  199. 


BKiaiW«ra*^^SW»rr^-' 


604 


INDEX. 


Batrr's  uranometry  (10S4),  430. 
Bbbr   and  Mabdlbr'b    map  of 

the  moon,  883. 
Bbbskl's  parallax  of  61    Cygni 

(1887).  476. 
BsflflEL's  work  on  the  theory  of 

Uranus,  866. 
BmiJk'B  comet,  404. 
Binary  ittan,  4S0. 
Binary  stars,  their  orbits,  403. 
Bodb'b  catalogue  of  stars,  485. 
BoDE's  bw  stated,  909. 
Bond's  disooveiy  of  the  dusky 

ring  of  Saturn.  18S0,  806. 
BoMD'a  obserrations  of  Dcmati's 

oomet.  880. 
BooiD'a  tbewy  of  the  oonstttutiou 

of  Saturn's  rings,  800. 
Boutabd'b  toblea  of  Uianus,  860. 
Bbadlbt  diaooven  aberration  in 

1720,240. 
Bkadubt's  method  of  ^e  and  ear 

observations  (1700).  79. 
Brif^tneas  of  aii  the  stars  of  each 

magnitude,  488. 
Calendar,  can  it  be  improved  r 

261. 
Calendar  of  the  Fraoch  Republic, 

202. 
Calmdars,  how  formed.  24a 
Calltfcs.  period  of,  208. 
Caasq^nOnian  (reflectiiig)  teieaoope, 

07. 
CAsann  diaoovers  foaraateUitea  of 

Saturn  (1084-1871).  880. 
CAsann's  value  of  the  aolar  panl- 

lax,  9'-8, 220. 
Cataloguea  (rf   atars,  goieral  ao- 

count,  484. 
Catakiguee  of  stars,  tbdr  arrange- 

ment,  200. 
Cavbudibh.  experiment  for  deter- 
mining the  denat^  of  the  earth, 
182. 
Celestial  mechanics  defined.  8. 
Celeetial  sphera.  14.  41. 
Central  edipae  of  the  sun,  177. 


Centra  of  gravity  of  the  solar  sys- 
tem, Wl». 

Centrifugal   force,   a  misnomer, 
210. 

Christie's  determination  of  mo- 
tion of  starsinlhieof  sight,  471. 

Chromatic  aberration  of  a  lens,  60. 

Chronograph  used  in  transit  ob- 
servations. 70. 

Chronology.  240. 

Chronometers.  70.  ' 

CuiiRAVT  predkits  the  return  of 
Halley's  oomet  (1709),  887. 

Ciuotu'a  elements  of  the  earth, 
202. 

Clocks,  70. 

Clusters  of  start  are  often  formed 
by  central  powers,  464. 

Coal-sacks  bi  ttw  mllhy  way,  410, 
480. 

Coma  of  a  comet.  888. 

Comets  defined,  268. 

Comets  formerly  inspired  terror, 
406-«. 

Comets,  general  account,  888. 

ComeU'  orbiu,  theory  of.  400. 

Cometo'  tails,  888. 

ComeU'  tails,  repulsive  force.  880. 

Cometa.  thdr  origin.  401. 

Comet8.tlieir  pbyskial  constitutton. 
808. 

Comets,  their  spectra.  898. 

Conjunction  (of  a  plaoet  with  the 
aun)  defined.  114 

Conimation  of  a  tnnait  instru- 
ment, 77. 

Conjug^  foci  of  a  lens  defined, 
05. 

Conateilatkms.  414 

Conrtdlattona.  in  parttenhw.  482. 
etteq. 

Oonstructkm  of  the  Hmvani,  478. 

Co-ordinatea  of  %  atar  dcAned.  41. 

OoPBLAiiD  obwrrai  spectrum  of 
new  atar  of  1878. 445. 

OoRini's  ofaeervatkns  of  spectrum 
of  new  star  of  1876. 445. 

'    .     ■  \ 


Ijiai 


at  gmvity  of  the  solar  sys- 

igal   force,    a   misnomer, 

ib'h  determination  of  mo- 

{  stars  in  line  of  siglit,  471 . 

tic  aberration  of  a  lens,  60. 

[;nph  used  in  transit  ob- 

ions,  "lO. 

ogjr.  845. 

neters,  70.  ' 

DT  predicts  the  return  of 

r'n  comet  (1750),  807. 

'■  elements  of  tlie  earth, 

TO. 

of  Stan  are  often  formed 

itral  powers,  464. 

ks  in  Um  taiVrj  way,  415, 

'  a  comet,  888. 

leflned.  268. 

formerly  inspired  terror, 

general  account,  888. 

orbiU,  theory  of,  400. 

tails,  888. 

tails,  repolslre  force,  885. 

ttadr  origin.  401. 

lieir  physical  oonstitutioa, 

their  spectra.  896. 

UoD  (of  a  plaoet  with  the 

iflned,  114 

ion  <rf  a  tnaait  Instru- 

77. 

te  foci  of  a  lens  defined. 

itioni.414. 

ttlo&a.  in  partloidar.  483, 

ition  of  the  Hmtw.  478. 
itea  of  •  atar  deAned.  41. 
n>  oiMavTM  spectrum  of 
ir  of  1878.445. 
ofaaemtions  of  spectrum 
star  of  1876,445. 


ti,jiwiiji»w.uji!iaw«aaiii 


INDEX. 


605 


CoKNii  ilcterminea  the  velocity  of 
li^'hl,  222. 

('urrection  of  a  clocli  defined,  73. 

C'u8niical  physics  defined.  8. 

Cosmogony  defined,  482. 

Corona,  its  spectrum,  805. 

Coronn  (the)  is  a  solar  appendage, 
802. 

Craters  of  the  moon,  838. 

Day,  how  subdivided  into  hours, 
etc.,  257. 

Days,  mean  solar,  and  solar,  259. 

Declination  of  a  star  defined,  20. 

Dispersive  powof  of  glass  defined, 
01. 

Distance  of  the  fixed  stars,  413, 
474. 

Distribution  of  the  stars,  480. 

Diurnal  motion,  10. 

Diurnal  paths  of  stars  are  circles 
12. 

Dominical  letter,  355. 

I3uNATi's  comet  (1858)^  407. 

Double  (and  multiple)  stars,  44". 

Double  stars,  their  colors.  452. 

£arth  (the),  a  sphere,  9. 

Earth  (the)  general  account  of,  188. 

Earth  (the)  is  a  point  in  compari> 
son  with  the  distance  of  the  fixed 
stars.  17. 

Earth  (the)  is  isolated  in  space,  10. 

Earth's  annual  revolution,  98. 

Earth's  atmosphere  at  least  lUO 
miles  in  heij^t.  880. 

Earth's  axis  renudns  pendlel  to  it- 
self during  an  annual  revolution, 
109, 110. 

Earth's  density.  188. 190. 

Earth's  dimensions,  801. 

Earth's  hitemal  heat.  408. 

Earth's  mass.  188. 

Earth's  mass  with  various  values 
of  sohur  parallax  (table),  380. 

Earth's  motion  of  rotation  proba- 
bly not  unfform,  148. 

Eartlis'  (the)  rel|Uion  to  the  heav- 
ens, 9. 


Earth's  rotation  maintained  by 
Arihtahoiiu.')  and  Timociiarih, 
and  opposed  by  Ptoi.kmv,  14. 

£iutb'8  surface  is  gradually  cool- 
ing, 498. 

Eccentrics  devised  by  the  ancienta 
to  account  for  the  irregularities 
of  planetary  motions.  121. 

Eclipses  of  the  moon,  170. 

Eclipses  of  the  sun  and  moon,  108. 

Eclipses  of  the  sun,  explanation, 
172. 

Eclipses  of  the  sun.  physical  phe- 
nomena, 207. 

Eclipses,  their  recurrence,  177. 

Ecliptic  defined,  100. 

Ecliptic  limits,  178. 

Elements  of  the  orbits  of  the  ma- 
jor planets,  376. 

Elliptic  motion  of  a  planet,  its 
mathematical  theory,  125. 

Elongation  (of  a  planet)  defined. 
114 

Encke'b  comet,  409. 

Enokb's  value  of  the  solar  paral- 
lax. 8" -857.  226. 

Ehoblmamn'b  photometric  meas- 
ures of  Jupiter's  satellites.  850. 

Envelopes  of  a  comet.  890. 

Epicycles,  their  theory,  110. 

Equation  of  time,  258. 

EquatMT  (celestial)  defined,  19,  34. 

Equatorial  telescope,  description 
of.  87. 

Equinoctkd  defined,  34 

Equinoctial  year,  807. 

Equinoxes.  104 

Equino::es;  how  determined,  105. 

Evection.  moon's  168. 

Eye-pieces  of  telescopes,  03. 

I^  (the  naked)  sees  about  3000 
stars.  411. 414 

FABBimis  observes  solar  soots 
(1611),  888. 

Figure  of  the  earth,  108. 

FizBAU  determines 
lij^t,  338. 


INDEX. 


506 

Fi.AMBTEEi>'«  catalogue  o(    8tar« 

PoWAUt.Tdetennlne«  the  velocity 

Future  of  the  solar  Bystem.  501 
Galaxy,  or  milky  way.  *"; 
GAUI.KO  olMorves  9ol8ri.pot«(l6U). 


Q  W«  dl«=overy  of  satellites 

o:srrriiSo:rSfthe.iiwy 

OrrSolrves    Neptune 

(1846).  867. 
Geodetic  surveys,  IW- 
Golden  number.  252. 
Gould's  urunometry,  48a. 
S«viS»tlon  extends  to  the  stars. 

OwvltoaJn  resides  lu  each  particle 

of  matter,  189. 
Gravitation.  Vrrestnal  (lU  laws). 

aiviiy    (on   the  ^U)  changes 

•with  the  latitude,  208. 

Greek  alphabet.  7. 

Gregorian  calendar,  2W. 
GvJiBN.hypotheacal  parallax  of 

GtSh^'  the  distribution  of  the 

stars.  489.  .  . 

HAi^utv  predicts  the  return  of  a 

comet  (1682).  897. 
HamJCy'b  comet.  898. 
HaWb  discovery  of  satellites  oi 

Mats.  888. 
Hall's  rototlon-period  of  Saturn, 

hShbbb  observes  the  spectrum 
of  the  corona  (1869).  8(». 

EauptpurMe  of  an  object  We.  61 
HAsSfl  value  of  the  solar  paral 

HL^Som^ofthenorthem 
sky.  417, 


Hklmholtz's  meamircB    of   the 
llniHs  of  imkwl  eye  vWon,  4. 

the8pectraofHtttr«(l7»8).408. 

Batellltei  of  Saturn  (1789),  360. 
Hbkbchbl  (W.).    discovers  two 
""JSS  of  Uranus  (1787)  m 

HEnflCHKL(W.)  discovers  Uramis 

HeSbMW.)  observes  double 

stars  (1780).  462. 
llBBflcBEL-fl  catalogues  of  nebu- 

las  457. 
Hkmciiel's  staf-gftuges.  479. 

Herbcbbl   (W.)  Slaves    "■ 
solar  system  Is  In  motion  (1788), 

.-  /  w  N  views  on  the 
Herbciielb  (W.)  view- 

nature  of  nebulas.  458. 
llEVBLiBB'fl  catalogue  of  9tor8.485 
Hul^B(0.  W.)  orbit  of  Donatis 

„S\g%.)  theory  of   Mer- 
nSs'lwlngs  of  Mars  (1666). 


HoSn(celestlal--^nslble)ofan 

nttserver  defined,  so. 
HoSb  guess  at  the  «.l«r  par- 

Ht"«^  of  a  Star  defined  25 
SZTi'B  investigation  of  orbit 

of  Blela's  comet,  404. 
HoGOWB'  determination  of  mo- 

♦J«n  of  BtMB  In  line  of  sight.  471. 
H?j;«.rt  observe  the  spectra 

of  nebulae  (1864).  465. 
H^^SHliervationsoftiiespec. 

traoftheptanete.870.«««?. 
HoooWB-  and  MiLLBB'B  obeerva- 
^tSTofspectrmnofnewstarof 

HlS«t^dMtLLEB'B  observa 

tions  of  stellar  spectra.  468. 
HiTGHKHB  discovers  a  sateUlte  of 

Saturn  (1665),  860. 


INDEX. 


507 


i,T7/B  mcamircB    of   the 
of  imkwl  eye  vWon,  4. 
Bi,    (W.).    ttrst    ol)H.TVe« 
ectraofHlttr«(17»8).  4«8. 
Eli  (W.),    discovers  two 
tei  of  Saturn  (1789).  860. 

an,  (W.).    discovers  two 
Ites  of  Uranus  (1787).  868. 
lEL  (W.)  discovers  Uranus 

).  862.  -     , , 

HEL  (W.)  observes  double 

(1780).  452. 

HBL's  catalogues  of  nebu- 

nEi/B  Star-gauges.  4TO. 
,HEL   (W.)  states    that  the 
r  system  Is  In  motion  (1788), 

ciiEL's  (W.)  views  on  the 

ire  of  nebulffi.  408. 
:u«s'scatalogueof  stars  «5^ 

'B  (G.  W.)  orbit  of  Donatl  s 
net,  409.  „ 

•b  (G.  W.)  theory  of    Mer 

S'9^rawlngsofMar.(1666). 

^n  (celestial-sensible)  of  an 

server  defined,  28. 

^x'B  guess  at  the  solar  par- 

f«S^  of  a  star  defined  25 
BBAW>'»  investigation  of  orbit 

r  Blela's  comet,  404. 
oowB'  determination  of  mo- 
on of  BtaiB  In  line  of  BlghvWl^ 
^WB  first  obeerveB  the  spectra 

.fnebuln  (1864).  465. 
lUr^lUvatlonBofJespoc- 

tra  of  the  planets.  870. «« «?• 
So«8'andMiLLKB'Bob«rva- 

JlonBof«pectrmnofnews.arof 

l^ii^dMt.i.EB'B  objerva 

tlons  of  stellar  spectra.  4«». 
["tohkhb  discovers  a  sateUite  of 

Batum  (1666).  860. 


HiivuiiKNS  discovers  laws  of  con- 
tra! forces.  136. 

lIuvoiiENS  discovers  the  neb- 
ula of  Orion  (10SO),  457. 

IIuYouKNs'  explanation  of  the 
appearances  of  Saturn's  rings 
(165r>),  866. 

IluYOiiENs'  guess  at  the  solar  par- 
allax, 220. 

IIuvoiiknb'  resolution  of  the  milky 
way.  410. 

Inferior  planets  defined,  116. 

Intramorcurial  planets,  822. 

Janbsbn  first  observes  solar  promi- 
nences in  daylight,  304. 

Jansben's  photographs  of  the  sun, 
281. 

Julian  year,  260. 

Jupiter,  general  account,  843. 

Jupiter's  rotation  time,  846 

Jupiter's  satellites,  846. 

Jupiter's  satellites,  their  elements, 
851. 

Kant'b  nebular  hypothesis,  492. 

Kepler's  idea  of  the  milky  way, 
416. 

Kepler's  laws  enunciated,  126. 

Kbflbr'b  laws  of  planetary  mo- 
tion, 122. 

Klbir,  photometric  measures  of 
Beta  Lyra,  442. 

Lacaille's  catalogues  of  nebula, 
467. 

Langlbt's  measures  of  solar  heat, 
288. 

Laholbt's  measures  of  the  heat 
from  sun  spots,  286. 

Laplacb  investigates  the  accelera- 
tion of  the  moon's  motion, 
146. 

Laplace's  nebular  hypothesis,  492. 

Laplacb'b  investigation  of  the 
constitution  of  Saturn's  rings, 
860. 

Laplacb'b  relations  between  the 
mean  motions  of  Juidter's  satel- 
Mtes,  849. 


Lahskll  discovers  Noptuno's  8at< 
ollite  (1847),  8(t9. 

Lahsell  dittcovers  two  satcHitcsof 
Uranus  (1847),  803. 

Latitude  (geocentric — geographic) 
of  a  place  on  the  earth  detlned, 
208. 

Latitude  of  a  point  on  the  earth  is 
measured  by  the  elevation  of  the 
pole,  21. 

Latitudes  and  longitudes  (celes- 
tial) defined,  112. 

Latitudes  (terrestrial),  how  deter- 
mined, 47,  48. 

La  Sage's  theory  of  the  cause  of 
gravitation,  150. 

Level  of  a  transit  instrument,  77. 

Lb  Verribh  computes  the  orbit  of 
meteoric  shower,  884. 

Lb  Yerribr's  researches  on  ttte 
theory  of  Mercury,  828. 

Lb  Yerribr's  work  on  pcrturba< 
tlons  of  Uranus,  866. 

Light-gathering  power  of  an  ob- 
ject glass,  66.     " 

Light-ratio  (of  stars)  is  about  2-5, 
417. 

Line  of  colllmatlon  of  a  telescope, 
69. 

Local  time,  82. 

LocKTBR's  discovery  of  a  spec- 
troscopic method,  804. 

Longitude  of  a  place  may  be  ex- 
pressed in  time,  83. 

Longitude  of  a  place  on  the  earth 
(how  determined),  84,  37,  88,  41. 

Iiongitudes  (celestial)  defined,  112. 

Lucid  stars  defined,  415. 

Lunar  phases,  nodea,  etc.  See 
Moon's  phases,  nodes,  etc. 

Maedlbb's  theory  of  a  central 
sun,  478. 

Magnifying  power  of  an  eyepiece, 
66. 

Magnifying  powers  (of  telescopes), 
which  can  be  advantageously 
employed,  68. 


1 
}  i 

i 


Vi 


»' 


508 


INDEX. 


Magnitudes  of  the  stan.  41(1. 

Mnjor  plnnots  defined,  208. 

Man,  iu  surface,  S86. 

Mars,  physical  description,  884. 

Murs,  rotatioD,  886. 

Man's   satellites    discoTered   by 

Hall  (1877),  888. 
Mabiub's  claim  to  discovery  of 

Jupiter's  satellites,  848. 
Maskrltnb  determines  the  den- 
sity of  the  earth,  103. 
Muss  and  density  of.  the  sun  and 

planets,  377. 
Mass  of  the  sun  In  relation  to 

masses  of  planets,  227. 
Masses  of  the  planets,  283. 
Maxwell's  theory  of  constitution 

of  Saturn's  rings,  860. 
Matbk  (C.)  flnt  observes  double 

Btnra  (1778),  463. 
Mean  solar  time  defined,  38. 
Measurement  of  a  degree  on  the 

earth's  surface,  301. 
Mercury's  atmosphere,  814. 
Mercury,  its   apparent  motions, 

810. 
Mercury,  its  aspects  and  rotation, 

818. 
Meridian  (celestial)  defined,  31, 25. 
Meridian  circle,  83. 
Meridfam  line  defined,  25. 
Meridians  (terrestrial)  defined,  21. 
McflBiBR's  catalogues  of  nebulae, 

457. 
Metonic  cycle,  251. 
Meteoric  showen,  880. 
Meteoric  showers,  orbits,  888. 
Meteora  and  comets,  theix  rehuton, 

888. 
Mcteore    first    visible  about  100 
miles  above  the  surface  of  the 
earth,  380. 
Meteon,  general  account,  375. 
Meteon,  their  cause,  877. 
Metric  equivalents,  8. 
Miohablsom  determines  the  ve- 
locity of  light  (1870).  9Sa. 


Micitrll's  researches  on  distri- 
butlon  of  Stan  (1777),  440. 

Micrometer  (filar),  description  and 
use,  89. 

Milky  way,  415. 

Milky  way,  its  general  shape  ac- 
cording to  IlRnsCHKL,  480. 

Minimum    Vimbile   of  telescopes 

(lable),  410. 
Minor  planeU  defined,  268. 
Minor  planets,   general  account, 

840. 
Mira  Oeti  (variable  star),  440. 
Mohammedan  calendar,  252. 
Months,  different  kinds,  340. 
Moon's  atmosphere,  881. 
Moon  craters,  820. 
Moon,  general  account,  826. 
Moon's  light  and  heat,  881. 
Moon's  light  l-618,000th  of   tlie 

sun's,  882. 
Moon's  motions  and  attraction, 

152. 
Moon's  nodes,  motion  of,  150. 
Moon's  perigee,  motion  of,  163. 
Moon's  phases,  154. 
Moon's  rotation,  164. 
Moon's  secular  acceleration,  146. 
Moon's  surface,  does  it  change, 

838. 
Moon's  surface,  its  character,  828. 
Motion  of  Stan   in   the  line  of 

sight,  470. 
Mountains  on  the    moon   often 

7000  metres  high,  880. 
Nadir  of  an  observer  defined,  33. 
Nautical  almanac  described,  363. 
Nebula  and  clusters,  how  distrib- 
uted, 465. 
Nebulas  and  dustors  in  general, 

457. 
Nebula  of  Orion,  the  first  telescopic 

nebuhi  discovered  (1650),  457. 
Nebulae,  their  spectra,  465. 
Nebular  hypothesis  stated,  407. 
N^une,  discoveiy  of  by  Lk  Vbr- 

BiBB  and  Adams  (1846),  867. « 


INDEX. 


S09 


:m.'b  roflcarchcs  on  dlRtri. 

>n  of  stars  (1777),  440. 

neter  (filar),  description  and 

80. 

way.  415. 

vf^y>  it"  gdoeml  shape  ac- 

ing  to  IlKitBcnsL,  4<M. 

vm    Vimbile   of  telescopca 

»),  419. 

planeto  defined,  268. 

planets,   general  account, 

eti  (variable  star),  440. 
imedan  calendar,  252. 
I,  different  kinds,  340. 

atmosphere,  881. 
raters,  820. 
general  account,  826. 
light  and  heat,  881. 

light  l-618,000th  of   tlie 
,882. 

motions  and  attraction, 

nodes,  motion  of,  150. 

perigee,  motion  of,  IdS. 

phases,  154. 

rotation,  164. 

secular  acceleration,  146. 

surface,  does  it  cliange, 

surface,  its  character,  828. 

of  stars   in   the  line  of 

470. 

Ins  on  the    moon   often 

netres  high,  880. 

t  an  observer  defined,  23. 

I  almanac  described,  268. 

and  clusters,  how  distrib- 

465. 

and  dusters  in  general, 

>t  Orion,  the  first  telescopic 
k  discovered  (1650),  457. 
their  spectra,  465. 
hypothesis  stated,  407. 
I,  discoveiy  of  by  Lk  Vbr- 
md  Adams  (1846),  867. » 


Neptune,   general    account,  365. 

Neptune's  satellite,  elements,  86U. 

New  star  of  1876  has  apparently 
becomn  n  plunvtary  nebula,  445. 

New  stars,  448. 

Nkwtok  (I.)  calculates  orbit  of 
comet  of  1680,  406. 

Nkwton  (I.)  Laws  of  Force, 
184. 

Newtonian  (reflecting)  telescope, 
00. 

Nkwtom'b  (I.)  investigation  of 
comet  orbits,  806. 

Newton's  (II.  A.)  researches  on 
meteors,  886. 

Newton's  (H.  A.)  theory  of  con- 
stitution of  comets,  804. 

Nucleus  of  a  comet,  888. 

Nucleus  of  a  solar  spot,  287. 

Nutation,  211. 

Objectives  (mathematical  theory), 
08. 

Objectives  or  object  glasses,  54. 

Obliquity  of  the  ecliptic,  100. 

OccultaUons  of  atars  by  the  nuwn 
(or  planets),  186. 

Olbbrb's  hypothesis  of  the  origin 
of  asteroids,  840,  8^. 

Olbbrs  predicts  the  return  of  a 
meteoric  shower,  881. 

Old  style  (in  dates),  254. 

Opposition  (of  a  planet  to  the  sun) 
defined,  115. 

Oppositions  of  Mars,  885. 

Parallax  of  Man,  220,  221. 

Paralhuc  of  the  sun,  216. 

Penumbra  of  the  earth'sor  moon's 
shadmr.  174. 

Photoepheraof  the  sun,  270. 

.PiOABDpubUslies  the  0(mntti»$anee 
det  Tern  (1670),  268. 

Pickbbiho'b  measures  of  solar 
light,  288. 

Planets,  their  relative  size  exhib- 
ited, 260. 

PouiiiUn's  measures  of  sokr  radi- 
ation, 286. 


Precession  of  the  equinoxes,  20(t, 
201). 

I'ToiiK.MY    determines   the  sohir 
parallax,  225. 

Parallax  (annual)  defined,  50. 

I*arallax  (equatorial  horizontal)  de- 
fined, 52. 

Parallax  (horizontal)  defined,  50. 

ParaUax  (in  general)  dcfinc«l,  60. 

Parallel  sphere  defined,  80. 

Parallels  of  declination  defined,  24. 

Parallax  of  the  stars,  general  ac- 
cotmt,  476. 

Peihck's  theory  of  the  constitu- 
tion of  Saturn's  rings,  850. 

Pendulums  of  astronomical  eluckti, 
71. 

Periodic  comets,  elements,  800. 

Perturbations  defined,  144. 
I  Perturbations  of  comets  by  Jupi- 
ter, 408. 

Photometer  defined,  417. 

PiAzzi  discovera  the  flnt  asteroid 
(1801),  840. 

Planetary  nebulie  defined,  459. 

Planets  ;  seven  bodies  so  called  by 
the  ancients,  96. 

Planets,  their  apparent  and   real 
motions,  lis. 

Planets,  Uieir   physical  constitu- 
tion, 870. 

Pleiades,  map  of,  ^5. 

Pleiades,  these  stan  are  physically 
connected,  449. 

Polar  distance  of  a  star,  26. 

Poles  of  the  celestial  sphere  de- 
fined, 14,  20,  24. 

Podtion  angle  defined,  00,  460. 

Power  of  telescopes,  its  limit,  828. 

Practical  astronomy  (defined),  2. 

Prime  vertical  of  an  observer  de- 
fined, 25. 

Problem  of  three  bodies,  141. 

Proctor's  map  of  distribution  of 
nebulse  and  clustere,  466. 

Proctor's  rotation  period  of  Mars, 


iiiMMy!'uijwim>^.j,aj. 


ft  10 


INDKX. 


Proper  motionN  r  f  sUirs,  473. 
I'ro|M'r  motion  of  tliu  huh.  47)). 
I'Toi.KMVM    euUilogiio    of    HUro, 

4l«. 
Proi.KMY  niaiutnins  tho  immova- 
bility of  tliu  cartl),  14. 
I'ytiiaiiohah'  concuption  of  eryn- 

tiilllno  HpliercH  for  llio  plaiiutH,  Uti. 
Ittuliant  point  of  meteor».  ]Ml. 
Hutu  of  a  clock  dcflned,  Ti. 
Kuiuling  microHCope,  81 ,  85. 
Hcd  Htars  (variable  sturs  often  red), 

442. 
Itvtlectiug  telescopes,  00. 
Kcflecting  tokwcopts,  thoir  advnn- 

tiigcB  and  diHmlvuntuges,  08,  (it). 
Refracting  telescopcH,  53. 
Uefraction  of  light  in  tho  atmos- 

])herc,  234. 
llefractive  power  of  a  lens  defined, 

05. 
Kef  nactive  power  of  glass  defined, 

01. 
Uelutivo  parallax  of  stars  defined, 

47b. 
Resisting  medium  in  spaco,  409. 
Reticle  of  a  transit  instrument,  70. 
lietrogradatlons  of  the  planeU  ex- 
plained, 118. 
Right  ascension  of  a  star  defined, 

22. 
Right   ascensions   of  stars,  how 

determined  by  observation,  31. 
Right  sphere  defined,  27. 
BiUen  on  the  moon,  880. 
RoBMBR  discovers  that  light  moves 

wogressively,  289. 
Rosbb's  measure  of  the  moon's 

heat,  882. 
8aro»  (the),  181. 
Batum,  general  account,  852. 
Saturn's  rings,  854. 
Saturn's  rings,  their  constitution, 

350. 
Saturn's  rings,  their  phases,  857. 
Saturn's  satellites,  800. 
Saturn's  satellites,  elements,  361. 


Havauv  first  compiilf*  orbit  of  u 
binitry  star  (1820),  450, 

H«'iiiAi>AiiKLi.rs  theory  of  rein- 
tious  of  comets  and  meteors, 
385. 

HciiMioT  discovers  new  star  in 
Cygnus  (1870),  445. 

Bciimii>t'h  observations  of  new 
star  of  18(MI,  444. 

SciioENFKi.D's  Durchmusteruug, 
Am. 

BciiHOBTKit's  observations  on  the 
rotation  of  Venus,  810. 

SciiwABB'a  observations  of  sua 
spote,  208. 

Seasons  (the),  108. 

Sbcciu's  estimate  of  solar  tempera- 
ture 0.100,000°  C,  280. 

Secciii's  types  of  star  spectra, 
408. 

Secondary  spectrum  of  object 
glasses  defined,  02. 

Secondb  pendulum,  lengtli,  formu- 
la for  it,  204. 

Secular  acceleration  of  the  moon's 
mean  motion,  140. 

Secular  perturbations  defined,  145. 

Semi  diameters  (apparent)  of  ce- 
lestial objects  defined,  52. 

Semi-diurnal  arcs  of  stars,  45. 

Sextant,  92. 

Shooting  stars,  877. 

Sidereal  system,  its  shape  accord- 
ing to  Hbrsobbl,  484. 

Sidereal  time  explained,  29. 

Sidereal  year,  207. 

Signs  of  the  Zodiac,  105. 

Silvered  glass  reflecting  telescopes, 
00. 

Sirius  is  about  500  times  brighter 
than  a  star  6">,  418. 

Stars  had  special  names  8000 
B.C.,  420. 

Solar  corona,  extent  of,  209. 
Solar  cycle,  255. 

Solar  heat  and  light,  its  cause,  806. 
Solar  heat,  its  amount,  284. 


IV  flmt  comimtnn  orMt  t»f  u 
ry  Htur  (lHa«).  4W». 
■■AiiKLi>rH    theory  of    rulii- 
s  uf    couiutM   auil   uic'lc'orH, 

DT  (liBCOvcrH    now  Btiir    iu 

nu8  (187U),  44.1. 

dt'h   obBurvutioua   of   nuw 

of  WW,  444. 

;npbi.d'8  Durchmustoruug, 

ibtkh'h  obHcrvatioua  on  thu 
tion  of  YenuH,  810. 
iBB'a   obaorvatloiu  of    sun 
8,  2»8. 
>8  (the),  108. 

ii'h  e8tiniato  of  sohir  tempera- 
O.IOO.OOO'  C,  280. 
fi'a  types  of   star  spectra, 

dary    Rpectrum    of    object 
ncH  dcflnod,  02. 
(L>  pendulum,  lengtli,  formu- 
3r  it,  204. 

ir  acceleration  of  the  moon's 
kQ  motion,  140. 
ir  perturbations  defined,  145. 
diameters  (apparent)  of  ce- 
ial  objects  defined,  52. 
diurnal  arcs  of  stars,  45. 
at,  02. 

ing  stars,  877. 

!al  system,  its  shape  accord- 
to  Hbrsobel,  484. 
eal  time  explained,  29. 
jal  year,  207. 
of  the  Zodiac,  105. 
'ed  gl&ss  reflecting  telescopes, 

I  is  about  500  times  brighter 
n  a  star  O",  418. 
had    special    names    8000 
.,  420. 

corona,  extent  of,  299. 
cycle,  256. 

heat  and  light,  its  cause,  806. 
heat,  its  amount,  284. 


INliKX. 


Ml 


Holiir  nintinn  In  npnno,  47.1, 

Holar piirulliix  from liiniirlni><pitili- 
ly.  'J3:«. 

Holur  |)ariillux  t'n>ni  MufH,  'J'iO. 

Bolar  piiriillux  from  velocity  of 
light,  222. 

Holur  pariillux,  hiatory  of  attempts 
to  (Ictermlni!  It,  228. 

Holur  purullux,  IIh  mouHiires,  210. 

Holur  purullux  prububly  uImmiI 
8"  Ml,  228. 

Holur  prominences  uro  gaseouM, 
80i). 

Holur  syHtem  deflnoti,  07. 

Holur  system,  description,  207. 

Holar  system,  its  future,  80t>,  601. 

Holur  temperature,  280. 

Hoistices,  108,  104. 

Spherical  aberration  of  a  lens,  01. 

Hpherical  astmnomy  (detined),  2. 

Spiral  nebulie  defined,  450. 

Star  clusters,  402. 

Star-gauges  of  Hbhsciibi.,  470.. 

Sta;-  magnitudes,  410. 

Stars  of  various  magnitudes,  how 
distributed,  486-7. 

Stars  Eien  by  the  naked  eye,  about 
2000,  411-414. 

Stars,  their  proper  motions,  472. 

Stars,  their  spectra,  408. 

Stbuvb's  (W.)  idea  of  the  distri- 
bution of  the  stars,  487. 

Sthcvb'b  (W.)  parallax  of  alpha 
Lym  (1838),  476. 

Stbuvb's  (W.)  search  for  [Nep- 
tune], 806. 

Struvb'b  (O.)  supposition  of 
changes  in  Saturn's  rings,  858. 

Suti'B  uranometry,  448. 

Summer  solstice,  110. 

Sun's  apparent  path,  101. 

Sun's  attraction  on  the  moon 
(and  earth),  156. 

Sun's  constitution,  805. 

Sun's  density,  280. 

Sun's  (the)  existence  cannot  be  in- 
definitely long,  406. 


Sun's  muss  over  700  times  fhul  of 

the  planets,  272. 
Huii'h    motion   unionjr    llio    NturH, 

lOl. 
Hun,  phyHicul  description,  278. 
Sun's  proper  motion,  47:i. 
Sun's  rotation  tinu',  al)out25iluyn, 

290. 
Hini -spots  nnd  fiu:ul(D,  2N7. 
Huu-Hpots  ure  continvd  to  certain 

purtH  of  tl'e  <ll8c,  380. 
Sun  r.pots,  cause  of  their  periodic 

up|)earui)ce  unknown,  2U4. 
Sun's  surface  is  griuiuully  cooling, 

494. 
Sun-spots,  their  nature,  200. 
Sun-spots,  their  periodicity,  202. 
Superior  plunets  (deflneti),  110. 
SwEPPNBono's  nebular  hypothe- 
sis, 4Mi. 
Swift's   supposed    discovery    of 

Vulcan,  «28. 
8ymbf>l8  used  in  astronomy,  0,  7. 
Telescopes,  their  advantages,  57, 

58. 
Telescopes  (reflecting),  00. 
Telescopes  (refracting),  6.1. 
Tempbl's  comet.  Its   relntion  to 

November  meteors,  884. 
Temporary  stars,  448. 
Theoretical  astronomy  (defined),  8. 
Tides,  105. 

Time  converted  into  arc,  82. 
TmocnAUis   maintains  tlie  rota- 
tion of  the  earth,  14. 
Total  solar  eclipses,  description  of, 

297. 
Transit  instrument,  74. 
Transit    instrument,  methods  of 

observation,  78. 
Transits  of  Mercury  and  Venus, 

818. 
Transits  of  Venus,  210. 
Triangulation,  199. 
Tropical  year,  207. 
Tycho  Bbahb's  catalogue  of  stars. 


I«  111 


mm 


II 


512 


INDEX. 


Tyciio  Brahe  observes  now  star 

of  1572,  443. 
Units  of  mass  and  Uiugth  enii)loye<l 

in  astronomy,  218. 
Univenal  gravitation   discovered 

toy  Newton,  149. 
Universal      gravitation     treated, 

131. 
Universe   (tlie)   general   account, 

411. 
Uranus,  general  account,  302. 
Variable  and  temporary  stars,  gen- 

cntl  account,  440. 
Variable  stars,  440. 
Variable  stars,  their  periods,  442. 
Variable  stars,  theories  of,  445. 
Variation,  moon's,  163. 
Velocity  of  light,  244. 
Venus's  atmosphere,  317. 
Venus,  its  apparent  motions,  810. 
Venus,   its  aspect   and    rotation, 

815. 
Vernal  equinox,  102, 110. 
Vernier,  82. 
Vogel's  determination  of  motion 

of  stars  in  line  of  sight,  471. 
Vookl'b  measures  of  solar  actinic 

force,  283. 
Voobl'b    observations    of    Mer- 
cury's spectrum,  314. 


Vooei/b  observations  of  spectrum 
of  new  star  of  1870,  445. 

Vowel's  ol>scrvaUous  of  the  spec- 
tra of  tbe  planets,  370,  et  »eq. 

Volcanoes  on  the  moon  supposed 
to  exist  by  HEitacnBL,  832. 

Vulcan,  322. 

Watbon'b  supposed  discovery  of 
Vulcan,  323,  834. 

Wave  and  armature  time,  40. 

Weight  of  a  body  defined,  189. 

Wilson 'b  theory  of  sun-spots,  290. 

Winter  solstice,  100. 

Wolf's  researches  on  sun-spots, 
295. 

Years,  different  kinds,  250. 

Young  observes  the  spectrum  of 
the  corona  (1860),  805. 

Zenith  defined,  19,  28. 

Zenith  telescope  described,  90. 

Zenith  telescope,  method  of  observ- 
ing, 92, 

Zodiac,  105. 

Zobllner'b  estimate  of  relative 
brightness  of  sua  and  planets. 
271. 

ZoBiiiiNER'B  measure  of  the  rela- 
tive brightness  of  sun  and  moon, 
332. 

Zone  observations,  85. 


•agyan*^;.;.-^ 


/b  obnervations  of  Bpectruni 

cw  star  of  1870,  44.'}. 

/b  olHwrvuUoits  of  tlic  spec- 

>f  tbe  plauets,  870,  et  tieq. 

io«8  on  the  moon  supposed 

cist  by  HERBcnBL,  832. 

1,  322. 

jn's  supposed  discovery  of 

:an,  828,  824. 

and  armature  time,  40. 

t  of  a  body  defined,  180. 

«'8  theory  of  sun-spots,  290. 

r  solstice,  100. 

's  researches  on  sun-spots. 


different  kinds,  250. 
>  observes  the  spectrum  of 
:orona  (1860),  805. 
defined,  19,  28. 
telescope  described,  00. 
telescope,  method  of  observ- 
92, 
,  105. 

ner's  estimate  of  relative 
itnesa  of  sun  and  planets, 

eter'b  measure  of  the  rela- 
brightncss  of  sun  and  moon, 

ibservations,  85. 


^^^ 


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